Tootfinder

This https://arxiv.org/abs/2404.02203 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

James-Stein Estimation in Gaussian Metrology : V2
The James-Stein estimator is a biased estimator -- for a finite number of samples its expected value is not the true mean. The maximum-likelihood estimator (MLE), is unbiased and asymptotically optimal. Yet, when estimating the mean of $3$ or more normally-distributed random variables, the James-Stein estimator has a smaller total (expected) error than the MLE. We introduce the James-Stein estimator to the field of quantum metrology, from both the frequentist and Bayesian perspectives. We chara…

This https://arxiv.org/abs/2404.11590 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCV_…

A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion
We present the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. STE is a fusion of the Tyler's M-estimator (TME) and a variant of the fast median subspace. Our theoretical analysis suggests that, under a common inlier-outlier model, STE can effectively recover the underlying subspace, even when it contains a smaller fraction of inliers relative to other methods in the field of robust subs…

This https://arxiv.org/abs/2309.08707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Fixed-b Asymptotics for Panel Models with Two-Way Clustering
This paper studies a cluster robust variance estimator proposed by Chiang, Hansen and Sasaki (2024) for linear panels. First, we show algebraically that this variance estimator (CHS estimator, hereafter) is a linear combination of three common variance estimators: the one-way unit cluster estimator, the "HAC of averages" estimator, and the "average of HACs" estimator. Based on this finding, we obtain a fixed-b asymptotic result for the CHS estimator and corresponding test statistics as the cros…

Rectangular Rotational Invariant Estimator for High-Rank Matrix Estimation
Farzad Pourkamali, Nicolas Macris
https://arxiv.org/abs/2403.04615 https://

Rectangular Rotational Invariant Estimator for High-Rank Matrix Estimation
We consider estimating a matrix from noisy observations coming from an arbitrary additive bi- rotational invariant perturbation. We propose an estimator which is optimal among the class of rectangular rotational invariant estimators and can be applied irrespective of the prior on the signal. For the particular case of Gaussian noise, we prove the optimality of the proposed estimator, and we find an explicit expression for the MMSE in terms of the limiting singular value distribution of the obse…

Quantile-respectful density estimation based on the Harrell-Davis quantile estimator
Andrey Akinshin
https://arxiv.org/abs/2404.03835 https://

Quantile-respectful density estimation based on the Harrell-Davis quantile estimator
Traditional density and quantile estimators are often inconsistent with each other. Their simultaneous usage may lead to inconsistent results. To address this issue, we propose a novel smooth density estimator that is naturally consistent with the Harrell-Davis quantile estimator. We also provide a jittering implementation to support discrete-continuous mixture distributions.

Testing an entropy estimator related to the dynamical state of galaxy clusters
J. M. Z\'uniga, C. A. Caretta, A. P. Gonz\'alez, E. Garc\'ia-Manzan\'arez
https://arxiv.org/abs/2403.04723

Testing an entropy estimator related to the dynamical state of galaxy clusters
We propose the entropy estimator $H_Z$, calculated from global dynamical parameters, in an attempt to capture the degree of evolution of galaxy systems. We assume that the observed (spatial and velocity) distributions of member galaxies in these systems evolve over time towards states of higher dynamical relaxation (higher entropy), becoming more random and homogeneous in virial equilibrium. Thus, the $H_Z$-entropy should correspond to the gravitacional assembly state of the systems. This was t…

Quickest Change Detection for Multiple Data Streams Using the James-Stein Estimator
Topi Halme, Venugopal V. Veeravalli, Visa Koivunen
https://arxiv.org/abs/2404.05486

Quickest Change Detection for Multiple Data Streams Using the James-Stein Estimator
The problem of quickest change detection is studied in the context of detecting an arbitrary unknown mean-shift in multiple independent Gaussian data streams. The James-Stein estimator is used in constructing detection schemes that exhibit strong detection performance both asymptotically and non-asymptotically. First, a James-Stein-based extension of the recently developed windowed CuSum test is introduced. Our results indicate that the proposed scheme constitutes a uniform improvement over its…

On the Optimal MMSE Channel Estimation for One-Bit Quantized MIMO Systems
Minhua Ding, Italo Atzeni, Antti T\"olli, A. Lee Swindlehurst
https://arxiv.org/abs/2404.05536

On the Optimal MMSE Channel Estimation for One-Bit Quantized MIMO Systems
This paper focuses on the minimum mean squared error (MMSE) channel estimator for multiple-input multiple-output (MIMO) systems with one-bit quantization at the receiver side. Despite its optimality and significance in estimation theory, the MMSE channel estimator has not been fully investigated in this context due to its general non-linearity and computational complexity. Instead, the typically suboptimal Bussgang linear MMSE (BLMMSE) estimator has been widely adopted. In this work, we develop…

This https://arxiv.org/abs/2309.13586 has been replaced.
link: https://scholar.google.com/scholar?q=a

Task-Oriented Dexterous Hand Pose Synthesis Using Differentiable Grasp Wrench Boundary Estimator
This work tackles the problem of task-oriented dexterous hand pose synthesis, which involves generating a static hand pose capable of applying a task-specific set of wrenches to manipulate objects. Unlike previous approaches that focus solely on force-closure grasps, which are unsuitable for non-prehensile manipulation tasks (\textit{e.g.}, turning a knob or pressing a button), we introduce a unified framework covering force-closure grasps, non-force-closure grasps, and a variety of non-prehens…

This https://arxiv.org/abs/2403.00764 has been replaced.
link: https://scholar.google.com/scholar?q=a

Optical-coherence-tomography-based deep-learning scatterer-density estimator using physically accurate noise model
We demonstrate a deep-learning-based scatterer density estimator (SDE) that processes local speckle patterns of optical coherence tomography (OCT) images and estimates the scatterer density behind each speckle pattern. The SDE is trained using large quantities of numerically simulated OCT images and their associated scatterer densities. The numerical simulation uses a noise model that incorporates the spatial properties of three types of noise, i.e., shot noise, relative-intensity noise, and no…

A posteriori error analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem
Yuan Wang, Sander Rhebergen
https://arxiv.org/abs/2404.04130

A posteriori error analysis of a space-time hybridizable discontinuous Galerkin method for the advection-diffusion problem
We present and analyze an a posteriori error estimator for a space-time hybridizable discontinuous Galerkin discretization of the time-dependent advection-diffusion problem. The residual-based error estimator is proven to be reliable and locally efficient. In the reliability analysis we combine a Peclet-robust coercivity type result and a saturation assumption, while local efficiency analysis is based on using bubble functions. The analysis considers both local space and time adaptivity and is …

This https://arxiv.org/abs/2008.08718 has been replaced.
link: https://scholar.google.com/scholar?q=a

Minimum discrepancy principle strategy for choosing $k$ in $k$-NN regression
We present a novel data-driven strategy to choose the hyperparameter $k$ in the $k$-NN regression estimator without using any hold-out data. We treat the problem of choosing the hyperparameter as an iterative procedure (over $k$) and propose using an easily implemented in practice strategy based on the idea of early stopping and the minimum discrepancy principle. This model selection strategy is proven to be minimax-optimal, under the fixed-design assumption on covariates, over some smoothness …

JDEC: JPEG Decoding via Enhanced Continuous Cosine Coefficients
Woo Kyoung Han, Sunghoon Im, Jaedeok Kim, Kyong Hwan Jin
https://arxiv.org/abs/2404.05558 h…

JDEC: JPEG Decoding via Enhanced Continuous Cosine Coefficients
We propose a practical approach to JPEG image decoding, utilizing a local implicit neural representation with continuous cosine formulation. The JPEG algorithm significantly quantizes discrete cosine transform (DCT) spectra to achieve a high compression rate, inevitably resulting in quality degradation while encoding an image. We have designed a continuous cosine spectrum estimator to address the quality degradation issue that restores the distorted spectrum. By leveraging local DCT formulation…

This https://arxiv.org/abs/2307.12615 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite-sum optimization: Adaptivity to smoothness and loopless variance reduction
For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past …

This https://arxiv.org/abs/2403.01150 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sequential Rotations and Error Analysis of a Simple Quaternion Estimator
Reference [1] introduces a novel closed-form quaternion estimator from two vector observations. The simplicity of the estimator sometimes yields singular expressions, the current annotation provides the simple rotation schemes for four singular cases. The estimator enables clear physical insights and a closed-form expression for the bias as a function of the quaternion error covariance matrix. The latter could be approximated up to second order with respect to the underlying measurement noise a…

Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation
Benedikt Fesl, Michael Baur, Florian Strasser, Michael Joham, Wolfgang Utschick
https://arxiv.org/abs/2403.03545

Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation
This work proposes a novel channel estimator based on diffusion models (DMs), one of the currently top-rated generative models. Contrary to related works utilizing generative priors, a lightweight convolutional neural network (CNN) with positional embedding of the signal-to-noise ratio (SNR) information is designed by learning the channel distribution in the sparse angular domain. Combined with an estimation strategy that avoids stochastic resampling and truncates reverse diffusion steps that a…

Estimation and Inference in Ultrahigh Dimensional Partially Linear Single-Index Models
Shijie Cui, Xu Guo, Zhe Zhang
https://arxiv.org/abs/2404.04471 https…

Estimation and Inference in Ultrahigh Dimensional Partially Linear Single-Index Models
This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference problem very challenging. In this paper, we first propose a profile partial penalized least squares estimator and establish the sparsity, consistency and asymptotic representation of the proposed estimator in ultrahigh dimensional setting. We then propose an $F$-t…

Stratifying on Treatment Status
Jinyong Hahn, John Ham, Geert Ridder, Shuyang Sheng
https://arxiv.org/abs/2404.04700 https://arxiv.org/pdf/2404.04700
arXiv:2404.04700v1 Announce Type: new
Abstract: We investigate the estimation of treatment effects from a sample that is stratified on the binary treatment status. In the case of unconfounded assignment where the potential outcomes are independent of the treatment given covariates, we show that standard estimators of the average treatment effect are inconsistent. In the case of an endogenous treatment and a binary instrument, we show that the IV estimator is inconsistent for the local average treatment effect. In both cases, we propose simple alternative estimators that are consistent in stratified samples, assuming that the fraction treated in the population is known or can be estimated.

On the Asymptotic Mean Square Error Optimality of Diffusion Probabilistic Models
Benedikt Fesl, Benedikt B\"ock, Florian Strasser, Michael Baur, Michael Joham, Wolfgang Utschick
https://arxiv.org/abs/2403.02957

On the Asymptotic Mean Square Error Optimality of Diffusion Probabilistic Models
Diffusion probabilistic models (DPMs) have recently shown great potential for denoising tasks. Despite their practical utility, there is a notable gap in their theoretical understanding. This paper contributes novel theoretical insights by rigorously proving the asymptotic convergence of a specific DPM denoising strategy to the mean square error (MSE)-optimal conditional mean estimator (CME) over a large number of diffusion steps. The studied DPM-based denoiser shares the training procedure of …

This https://arxiv.org/abs/2102.13273 has been replaced.
link: https://scholar.google.com/scholar?q=a

Application-Driven Learning: A Closed-Loop Prediction and Optimization Approach Applied to Dynamic Reserves and Demand Forecasting
Forecasting and decision-making are generally modeled as two sequential steps with no feedback, following an open-loop approach. In this paper, we present application-driven learning, a new closed-loop framework in which the processes of forecasting and decision-making are merged and co-optimized through a bilevel optimization problem. We present our methodology in a general format and prove that the solution converges to the best estimator in terms of the expected cost of the selected applicat…

This https://arxiv.org/abs/2302.14119 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Double-loop randomized quasi-Monte Carlo estimator for nested integration
Characterized by an outer integral connected to an inner integral through a nonlinear function, nested integration is a challenging problem in various fields, such as engineering and mathematical finance. The available numerical methods for nested integration based on Monte Carlo (MC) methods can be prohibitively expensive owing to the error propagating from the inner to the outer integral. Attempts to enhance the efficiency of these approximations using the quasi-MC (QMC) or randomized QMC (rQ…

This https://arxiv.org/abs/2402.15242 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

On the existence of unbiased resilient estimators in discrete quantum systems
Cramér-Rao constitutes a crucial lower bound for the mean squared error of an estimator in frequentist parameter estimation, albeit paradoxically demanding highly accurate prior knowledge of the parameter to be estimated. Indeed, this information is needed to construct the optimal unbiased estimator, which is highly dependent on the parameter. Conversely, Bhattacharyya bounds result in a more resilient estimation about prior accuracy by imposing additional constraints on the estimator. Initial…

On the Use of Autoregressive Methods for Audio Inpainting
Ond\v{r}ej Mokr\'y, Pavel Rajmic
https://arxiv.org/abs/2403.04433 https://

On the Use of Autoregressive Methods for Audio Inpainting
The paper presents an evaluation of popular audio inpainting methods based on autoregressive modelling, namely, extrapolation-based and Janssen methods. A novel variant of the Janssen method suitable for gap inpainting is also proposed. The main differences between the particular popular approaches are pointed out, and a mid-scale computational experiment is presented. The results demonstrate the importance of the choice of the AR model estimator and the suitability of the new gap-wise Janssen …

This https://arxiv.org/abs/2401.06326 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Optimal linear prediction with functional observations: Why you can use a simple post-dimension reduction estimator
This paper investigates optimal linear prediction for a random function in an infinite-dimensional Hilbert space. We analyze the mean square prediction error (MSPE) associated with a linear predictor, revealing that non-unique solutions that minimize the MSPE generally exist and consistent estimation is often impossible even if a unique solution exists. However, we show that defining asymptotically optimal linear operators, whose empirical MSPEs approach the minimal achievable level, is feasibl…

This https://arxiv.org/abs/2403.00967 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic expansion of the drift estimator for the fractional Ornstein-Uhlenbeck process
We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the authors [26]. The central limit theorem in the principal part of the expansion has the classical scaling T^{1/2}. However, the asymptotic expansion formula is a complex in that the order of the correction term becomes the classical T^{-1/2} for H in (1/2,5/8), bu…

Stratifying on Treatment Status
Jinyong Hahn, John Ham, Geert Ridder, Shuyang Sheng
https://arxiv.org/abs/2404.04700 https://arxiv.org/pdf/2404.04700
arXiv:2404.04700v1 Announce Type: new
Abstract: We investigate the estimation of treatment effects from a sample that is stratified on the binary treatment status. In the case of unconfounded assignment where the potential outcomes are independent of the treatment given covariates, we show that standard estimators of the average treatment effect are inconsistent. In the case of an endogenous treatment and a binary instrument, we show that the IV estimator is inconsistent for the local average treatment effect. In both cases, we propose simple alternative estimators that are consistent in stratified samples, assuming that the fraction treated in the population is known or can be estimated.

This https://arxiv.org/abs/2312.13859 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Nonlinear Functional Estimation: Functional Detectability and Full Information Estimation
We consider the design of functional estimators, i.e., approaches to compute an estimate of a nonlinear function of the state of a general nonlinear dynamical system subject to process noise based on noisy output measurements. To this end, we introduce a novel functional detectability notion in the form of incremental input/output-to-output stability ($δ$-IOOS). We show that $δ$-IOOS is a necessary condition for the existence of a functional estimator satisfying an input-to-output type stabil…

This https://arxiv.org/abs/2312.08246 has been replaced.
initial toot: https://mastoxiv.page/@…

An estimator of entropy production for partially accessible Markov networks based on the observation of blurred transitions
A central task in stochastic thermodynamics is the estimation of entropy production for partially accessible Markov networks. We establish an effective transition-based description for such networks with transitions that are not distinguishable and therefore blurred for an external observer. We demonstrate that, in contrast to a description based on fully resolved transitions, this effective description is typically non-Markovian at any point in time. Starting from an information-theoretic boun…

Doubly-Robust Off-Policy Evaluation with Estimated Logging Policy
Kyungbok Lee, Myunghee Cho Paik
https://arxiv.org/abs/2404.01830 https://

Doubly-Robust Off-Policy Evaluation with Estimated Logging Policy
We introduce a novel doubly-robust (DR) off-policy evaluation (OPE) estimator for Markov decision processes, DRUnknown, designed for situations where both the logging policy and the value function are unknown. The proposed estimator initially estimates the logging policy and then estimates the value function model by minimizing the asymptotic variance of the estimator while considering the estimating effect of the logging policy. When the logging policy model is correctly specified, DRUnknown a…

This https://arxiv.org/abs/2302.14119 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Double-loop randomized quasi-Monte Carlo estimator for nested integration
Characterized by an outer integral connected to an inner integral through a nonlinear function, nested integration is a challenging problem in various fields, such as engineering and mathematical finance. The available numerical methods for nested integration based on Monte Carlo (MC) methods can be prohibitively expensive owing to the error propagating from the inner to the outer integral. Attempts to enhance the efficiency of these approximations using the quasi-MC (QMC) or randomized QMC (rQ…

Fault Detection and Monitoring using an Information-Driven Strategy: Method, Theory, and Application
Camilo Ram\'irez, Jorge F. Silva, Ferhat Tamssaouet, Tom\'as Rojas, Marcos E. Orchard
https://arxiv.org/abs/2405.03667

Fault Detection and Monitoring using an Information-Driven Strategy: Method, Theory, and Application
The ability to detect when a system undergoes an incipient fault is of paramount importance in preventing a critical failure. In this work, we propose an information-driven fault detection method based on a novel concept drift detector. The method is tailored to identifying drifts in input-output relationships of additive noise models (i.e., model drifts) and is based on a distribution-free mutual information (MI) estimator. Our scheme does not require prior faulty examples and can be applied d…

This https://arxiv.org/abs/2311.01336 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Covariance estimation using h-statistics in Monte Carlo and multilevel Monte Carlo methods
We present novel Monte Carlo (MC) and multilevel Monte Carlo (MLMC) methods to determine the unbiased covariance of random variables using h-statistics. The advantage of this procedure lies in the unbiased construction of the estimator's mean square error in a closed form. This is in contrast to conventional MC and MLMC covariance estimators, which are based on biased mean square errors defined solely by upper bounds, particularly within the MLMC. The numerical results of the algorithms are dem…

Robust covariance estimation and explainable outlier detection for matrix-valued data
Marcus Mayrhofer, Una Radoji\v{c}i\'c, Peter Filzmoser
https://arxiv.org/abs/2403.03975 <…

Robust covariance estimation and explainable outlier detection for matrix-valued data
The minimum covariance determinant (MCD) estimator is a popular method for robustly estimating the mean and covariance of multivariate data. We extend the MCD to the setting where the observations are matrices rather than vectors and introduce the matrix minimum covariance determinant (MMCD) estimators for robust parameter estimation. These estimators hold equivariance properties, achieve a high breakdown point, and are consistent under elliptical matrix-variate distributions. We have also deve…

Regularized Q-learning through Robust Averaging
Peter Schmitt-F\"orster, Tobias Sutter
https://arxiv.org/abs/2405.02201 https://…

Regularized Q-learning through Robust Averaging
We propose a new Q-learning variant, called 2RA Q-learning, that addresses some weaknesses of existing Q-learning methods in a principled manner. One such weakness is an underlying estimation bias which cannot be controlled and often results in poor performance. We propose a distributionally robust estimator for the maximum expected value term, which allows us to precisely control the level of estimation bias introduced. The distributionally robust estimator admits a closed-form solution such t…

EAD-VC: Enhancing Speech Auto-Disentanglement for Voice Conversion with IFUB Estimator and Joint Text-Guided Consistent Learning
Ziqi Liang, Jianzong Wang, Xulong Zhang, Yong Zhang, Ning Cheng, Jing Xiao
https://arxiv.org/abs/2404.19212

EAD-VC: Enhancing Speech Auto-Disentanglement for Voice Conversion with IFUB Estimator and Joint Text-Guided Consistent Learning
Using unsupervised learning to disentangle speech into content, rhythm, pitch, and timbre for voice conversion has become a hot research topic. Existing works generally take into account disentangling speech components through human-crafted bottleneck features which can not achieve sufficient information disentangling, while pitch and rhythm may still be mixed together. There is a risk of information overlap in the disentangling process which results in less speech naturalness. To overcome such…

Context-dependent Causality (the Non-Nonotonic Case)
Nir Billfeld, Moshe Kim
https://arxiv.org/abs/2404.05021 https://arxiv.org/pdf/2…

Context-dependent Causality (the Non-Nonotonic Case)
We develop a novel identification strategy as well as a new estimator for context-dependent causal inference in non-parametric triangular models with non-separable disturbances. Departing from the common practice, our analysis does not rely on the strict monotonicity assumption. Our key contribution lies in leveraging on diffusion models to formulate the structural equations as a system evolving from noise accumulation to account for the influence of the latent context (confounder) on the outco…

This https://arxiv.org/abs/2304.13794 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hölder regularity and roughness: construction and examples
We study how to construct a stochastic process on a finite interval with given `roughness' and finite joint moments of marginal distributions. We first extend Ciesielski's isomorphism along a general sequence of partitions, and provide a characterization of Hölder regularity of a function in terms of its Schauder coefficients. Using this characterization we provide a better (pathwise) estimator of Hölder exponent. As an additional application, we construct fake (fractional) Brownian motions w…

Distributed variable screening for generalized linear models
Tianbo Diao, Lianqiang Qu, Bo Li, Liuquan Sun
https://arxiv.org/abs/2405.04254 https://…

Distributed variable screening for generalized linear models
In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed method selects relevant covariates by using a sparsity-restricted surrogate likelihood estimator. It takes into account the joint effects of the covariates rather than just the marginal effect, and this characteristic enhances the reliability of the screening r…

Precision-based designs for sequential randomized experiments
Mattias Nordin, M{\aa}rten Schultzberg
https://arxiv.org/abs/2405.03487 https://

Precision-based designs for sequential randomized experiments
In this paper, we consider an experimental setting where units enter the experiment sequentially. Our goal is to form stopping rules which lead to estimators of treatment effects with a given precision. We propose a fixed-width confidence interval design (FWCID) where the experiment terminates once a pre-specified confidence interval width is achieved. We show that under this design, the difference-in-means estimator is a consistent estimator of the average treatment effect and standard confide…

Unbiased Markov chain quasi-Monte Carlo for Gibbs samplers
Jiarui Du, Zhijian He
https://arxiv.org/abs/2403.04407 https://arxiv.org/p…

Unbiased Markov chain quasi-Monte Carlo for Gibbs samplers
In statistical analysis, Monte Carlo (MC) stands as a classical numerical integration method. When encountering challenging sample problem, Markov chain Monte Carlo (MCMC) is a commonly employed method. However, the MCMC estimator is biased after a fixed number of iterations. Unbiased MCMC, an advancement achieved through coupling techniques, addresses this bias issue in MCMC. However, its variance retains the traditional $O(N^{-1/2})$ convergence rate. Quasi-Monte Carlo (QMC), known for its hi…

This https://arxiv.org/abs/2303.12213 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Alpha shapes in kernel density estimation
For every Gaussian kernel density estimator $f(x)=\sum_i a_i \exp(-\lVert x-x_i\rVert^2/2h^2)$ associated to a point cloud $\mathcal{D}=\{x_1,...,x_N\}\subset \mathbb{R}^d$, we define a nested family of closed subspaces $\mathcal{S}(a)\subset\mathbb{R}^d$, which we interpret as a continuous version of an alpha shape. Using arguments based on Fenchel duality, we prove that $\mathcal{S}(a)$ is homotopy equivalent to the superlevel set $\mathcal{L}(a)=f^{-1}[e^{-a},\infty)$, and that $\mathcal{L}(…

Hybrid low-dimensional limiting state of charge estimator for multi-cell lithium-ion batteries
Mira Khalil, Romain Postoyan, St\'ephane Ra\"el, Dragan Ne\v{s}i\'c
https://arxiv.org/abs/2403.16555

Hybrid low-dimensional limiting state of charge estimator for multi-cell lithium-ion batteries
The state of charge (SOC) of lithium-ion batteries needs to be accurately estimated for safety and reliability purposes. For battery packs made of a large number of cells, it is not always feasible to design one SOC estimator per cell due to limited computational resources. Instead, only the minimum and the maximum SOC need to be estimated. The challenge is that the cells having minimum and maximum SOC typically change over time. In this context, we present a low-dimensional hybrid estimator of…

Kinetic Sunyaev Zel'dovich velocity reconstruction from Planck and unWISE
Richard Bloch, Matthew C. Johnson
https://arxiv.org/abs/2405.00809 https://…

Kinetic Sunyaev Zel'dovich velocity reconstruction from Planck and unWISE
The kinetic Sunyaev Zel'dovich (kSZ) effect is a blackbody cosmic microwave background (CMB) temperature anisotropy induced by Thomson scattering off free electrons in bulk motion with respect to the CMB rest frame. The statistically anisotropic cross-correlation between the CMB and galaxy surveys encodes the radial bulk velocity (more generally, the remote dipole field), which can be efficiently reconstructed using a quadratic estimator. Here, we develop and implement a quadratic estimator for…

This https://arxiv.org/abs/2405.04254 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Distributed variable screening for generalized linear models
In this article, we develop a distributed variable screening method for generalized linear models. This method is designed to handle situations where both the sample size and the number of covariates are large. Specifically, the proposed method selects relevant covariates by using a sparsity-restricted surrogate likelihood estimator. It takes into account the joint effects of the covariates rather than just the marginal effect, and this characteristic enhances the reliability of the screening r…

Two-way Fixed Effects and Differences-in-Differences Estimators in Heterogeneous Adoption Designs
Cl\'ement de Chaisemartin, Xavier D'Haultf{\oe}uille
https://arxiv.org/abs/2405.04465

Two-way Fixed Effects and Differences-in-Differences Estimators in Heterogeneous Adoption Designs
We consider treatment-effect estimation under a parallel trends assumption, in heterogeneous adoption designs where no unit is treated at period one, and units receive a weakly positive dose at period two. First, we develop a test of the assumption that the treatment effect is mean independent of the treatment, under which the commonly-used two-way-fixed-effects estimator is consistent. When this test is rejected, we propose alternative, robust estimators. If there are stayers with a period-two…

This https://arxiv.org/abs/2309.13239 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On optimality of Mallows model averaging
In the past decades, model averaging (MA) has attracted much attention as it has emerged as an alternative tool to the model selection (MS) statistical approach. Hansen [Econometrica 75 (2007) 1175--1189] introduced a Mallows model averaging (MMA) method with model weights selected by minimizing a Mallows' $C_p$ criterion. The main theoretical justification for MMA is an asymptotic optimality (AOP), which states that the risk/loss of the resulting MA estimator is asymptotically equivalent to th…

This https://arxiv.org/abs/2306.02742 has been replaced.
link: https://scholar.google.com/scholar?q=a

Enhanced Robust Motion Control based on Unknown System Dynamics Estimator for Robot Manipulators
To achieve high-accuracy manipulation in the presence of unknown disturbances, we propose two novel efficient and robust motion control schemes for high-dimensional robot manipulators. Both controllers incorporate an unknown system dynamics estimator (USDE) to estimate disturbances without requiring acceleration signals and the inverse of inertia matrix. Then, based on the USDE framework, an adaptive-gain controller and a super-twisting sliding mode controller are designed to speed up the conve…

This https://arxiv.org/abs/2012.00180 has been replaced.
link: https://scholar.google.com/scholar?q=a

Anisotropic local constant smoothing for change-point regression function estimation
Understanding forest fire spread in any region of Canada is critical to promoting forest health, and protecting human life and infrastructure. Quantifying fire spread from noisy images, where regions of a fire are separated by change-point boundaries, is critical to faithfully estimating fire spread rates. In this research, we develop a statistically consistent smooth estimator that allows us to denoise fire spread imagery from micro-fire experiments. We develop an anisotropic smoothing method …

Strang Splitting for Parametric Inference in Second-order Stochastic Differential Equations
Predrag Pilipovic, Adeline Samson, Susanne Ditlevsen
https://arxiv.org/abs/2405.03606 <…

Strang Splitting for Parametric Inference in Second-order Stochastic Differential Equations
We address parameter estimation in second-order stochastic differential equations (SDEs), prevalent in physics, biology, and ecology. Second-order SDE is converted to a first-order system by introducing an auxiliary velocity variable raising two main challenges. First, the system is hypoelliptic since the noise affects only the velocity, making the Euler-Maruyama estimator ill-conditioned. To overcome that, we propose an estimator based on the Strang splitting scheme. Second, since the velocity…

Beyond MMSE: Rank-1 Subspace Channel Estimator for Massive MIMO Systems
Bin Li, Ziping Wei, Shaoshi Yang, Yang Zhang, Jun Zhang, Chenglin Zhao, Sheng Chen
https://arxiv.org/abs/2404.13603

Beyond MMSE: Rank-1 Subspace Channel Estimator for Massive MIMO Systems
To glean the benefits offered by massive multi-input multi-output (MIMO) systems, channel state information must be accurately acquired. Despite the high accuracy, the computational complexity of classical linear minimum mean squared error (MMSE) estimator becomes prohibitively high in the context of massive MIMO, while the other low-complexity methods degrade the estimation accuracy seriously. In this paper, we develop a novel rank-1 subspace channel estimator to approximate the maximum likeli…

This https://arxiv.org/abs/2307.05352 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Leveraging Variational Autoencoders for Parameterized MMSE Estimation
In this manuscript, we propose to use a variational autoencoder-based framework for parameterizing a conditional linear minimum mean squared error estimator. The variational autoencoder models the underlying unknown data distribution as conditionally Gaussian, yielding the conditional first and second moments of the estimand, given a noisy observation. The derived estimator is shown to approximate the minimum mean squared error estimator by utilizing the variational autoencoder as a generative …

Inference for non-stationary time series quantile regression with inequality constraints
Yuan Sun, Zhou Zhou
https://arxiv.org/abs/2404.03837 https://

Inference for non-stationary time series quantile regression with inequality constraints
We consider parameter inference for linear quantile regression with non-stationary predictors and errors, where the regression parameters are subject to inequality constraints. We show that the constrained quantile coefficient estimators are asymptotically equivalent to the metric projections of the unconstrained estimator onto the constrained parameter space. Utilizing a geometry-invariant property of this projection operation, we propose inference procedures - the Wald, likelihood ratio, and …

This https://arxiv.org/abs/2402.17886 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Zeroth-Order Sampling Methods for Non-Log-Concave Distributions: Alleviating Metastability by Denoising Diffusion
This paper considers the problem of sampling from non-logconcave distribution, based on queries of its unnormalized density. It first describes a framework, Diffusion Monte Carlo (DMC), based on the simulation of a denoising diffusion process with its score function approximated by a generic Monte Carlo estimator. DMC is an oracle-based meta-algorithm, where its oracle is the assumed access to samples that generate a Monte Carlo score estimator. Then we provide an implementation of this oracle,…

This https://arxiv.org/abs/2303.12213 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Alpha shapes in kernel density estimation
For every Gaussian kernel density estimator $f(x)=\sum_i a_i \exp(-\lVert x-x_i\rVert^2/2h^2)$ associated to a point cloud $\mathcal{D}=\{x_1,...,x_N\}\subset \mathbb{R}^d$, we define a nested family of closed subspaces $\mathcal{S}(a)\subset\mathbb{R}^d$, which we interpret as a continuous version of an alpha shape. Using arguments based on Fenchel duality, we prove that $\mathcal{S}(a)$ is homotopy equivalent to the superlevel set $\mathcal{L}(a)=f^{-1}[e^{-a},\infty)$, and that $\mathcal{L}(…

Maximum A Posteriori Ly-alpha Estimator (MAPLE): Band-power and covariance estimation of the 3D Ly-alpha forest power spectrum
Benjamin Horowitz, Roger de Belsunce, Zarija Lukic
https://arxiv.org/abs/2403.17294

Maximum A Posteriori Ly-alpha Estimator (MAPLE): Band-power and covariance estimation of the 3D Ly-alpha forest power spectrum
We present a novel maximum a posteriori estimator to jointly estimate band-powers and the covariance of the three-dimensional power spectrum (P3D) of Lyman-alpha forest flux fluctuations, called MAPLE. Our Wiener-filter based algorithm reconstructs a window-deconvolved P3D in the presence of complex survey geometries typical for Lyman-alpha surveys that are sparsely sampled transverse to and densely sampled along the line-of-sight. We demonstrate our method on idealized Gaussian random fields w…

This https://arxiv.org/abs/2311.02732 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Solving High Dimensional Partial Differential Equations Using Tensor Neural Network and A Posteriori Error Estimators
In this paper, based on the combination of tensor neural network and a posteriori error estimator, a novel type of machine learning method is proposed to solve high-dimensional boundary value problems with homogeneous and non-homogeneous Dirichlet or Neumann type of boundary conditions and eigenvalue problems of the second-order elliptic operator. The most important advantage of the tensor neural network is that the high dimensional integrations of tensor neural networks can be computed with hi…

Warped Kernel Estimator for I.I.D. Paths of Diffusion Processes
Nicolas Marie, Am\'elie Rosier
https://arxiv.org/abs/2403.00186 https://

Warped Kernel Estimator for I.I.D. Paths of Diffusion Processes
This paper deals with a nonparametric warped kernel estimator $\widehat b$ of the drift function computed from independent continuous observations of a diffusion process. A risk bound on $\widehat b$ is established. The paper also deals with an extension of the PCO bandwidth selection method for $\widehat b$. Finally, some numerical experiments are provided.

This https://arxiv.org/abs/2107.13737 has been replaced.
link: https://scholar.google.com/scholar?q=a

Design-Robust Two-Way-Fixed-Effects Regression For Panel Data
We propose a new estimator for average causal effects of a binary treatment with panel data in settings with general treatment patterns. Our approach augments the popular two-way-fixed-effects specification with unit-specific weights that arise from a model for the assignment mechanism. We show how to construct these weights in various settings, including the staggered adoption setting, where units opt into the treatment sequentially but permanently. The resulting estimator converges to an aver…

This https://arxiv.org/abs/2011.01718 has been replaced.
link: https://scholar.google.com/scholar?q=a

Multi-Iteration Stochastic Optimizers
We here introduce Multi-Iteration Stochastic Optimizers, a novel class of first-order stochastic optimizers where the relative $L^2$ error is estimated and controlled using successive control variates along the path of iterations. By exploiting the correlation between iterates, control variates may reduce the estimator's variance so that an accurate estimation of the mean gradient becomes computationally affordable. We name the estimator of the mean gradient Multi-Iteration stochastiC Estimator…

This https://arxiv.org/abs/2111.09971 has been replaced.
link: https://scholar.google.com/scholar?q=a

Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations
This paper addresses learning safe output feedback control laws from partial observations of expert demonstrations. We assume that a model of the system dynamics and a state estimator are available along with corresponding error bounds, e.g., estimated from data in practice. We first propose robust output control barrier functions (ROCBFs) as a means to guarantee safety, as defined through controlled forward invariance of a safe set. We then formulate an optimization problem to learn ROCBFs fro…

Small diffusivity asymptotics for a linear parabolic SPDE in two space dimensions
Yozo Tonaki, Yusuke Kaino, Masayuki Uchida
https://arxiv.org/abs/2404.02513

Small diffusivity asymptotics for a linear parabolic SPDE in two space dimensions
We consider parameter estimation of the reaction term for a second order linear parabolic stochastic partial differential equation in two space dimensions driven by a $Q$-Wiener process under small diffusivity. We first construct an estimator of the reaction parameter based on continuous spatio-temporal data, and then derive an estimator of the reaction parameter based on high frequency spatio-temporal data by discretizing the estimator based on the continuous data. We show that the estimators …

Pilot Signal and Channel Estimator Co-Design for Hybrid-Field XL-MIMO
Yoonseong Kang, Hyowoon Seo, Wan Choi
https://arxiv.org/abs/2403.19105 https://

Pilot Signal and Channel Estimator Co-Design for Hybrid-Field XL-MIMO
This paper addresses the intricate task of hybrid-field channel estimation in extremely large-scale MIMO (XL-MIMO) systems, critical for the progression of 6G communications. Within these systems, comprising a line-of-sight (LoS) channel component alongside far-field and near-field scattering channel components, our objective is to tackle the channel estimation challenge. We encounter two central hurdles for ensuring dependable sparse channel recovery: the design of pilot signals and channel es…

Traj-LIO: A Resilient Multi-LiDAR Multi-IMU State Estimator Through Sparse Gaussian Process
Xin Zheng, Jianke Zhu
https://arxiv.org/abs/2402.09189 https://…

Traj-LIO: A Resilient Multi-LiDAR Multi-IMU State Estimator Through Sparse Gaussian Process
Nowadays, sensor suits have been equipped with redundant LiDARs and IMUs to mitigate the risks associated with sensor failure. It is challenging for the previous discrete-time and IMU-driven kinematic systems to incorporate multiple asynchronized sensors, which are susceptible to abnormal IMU data. To address these limitations, we introduce a multi-LiDAR multi-IMU state estimator by taking advantage of Gaussian Process (GP) that predicts a non-parametric continuous-time trajectory to capture se…

Decision Transformer as a Foundation Model for Partially Observable Continuous Control
Xiangyuan Zhang, Weichao Mao, Haoran Qiu, Tamer Ba\c{s}ar
https://arxiv.org/abs/2404.02407 <…

Decision Transformer as a Foundation Model for Partially Observable Continuous Control
Closed-loop control of nonlinear dynamical systems with partial-state observability demands expert knowledge of a diverse, less standardized set of theoretical tools. Moreover, it requires a delicate integration of controller and estimator designs to achieve the desired system behavior. To establish a general controller synthesis framework, we explore the Decision Transformer (DT) architecture. Specifically, we first frame the control task as predicting the current optimal action based on past …

This https://arxiv.org/abs/2306.00296 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Inference in Predictive Quantile Regressions
This paper studies inference in predictive quantile regressions when the predictive regressor has a near-unit root. We derive asymptotic distributions for the quantile regression estimator and its heteroskedasticity and autocorrelation consistent (HAC) t-statistic in terms of functionals of Ornstein-Uhlenbeck processes. We then propose a switching-fully modified (FM) predictive test for quantile predictability. The proposed test employs an FM style correction with a Bonferroni bound for the loc…

Distributed Iterative Hard Thresholding for Variable Selection in Tobit Models
Changxin Yang, Zhongyi Zhu, Heng Lian
https://arxiv.org/abs/2405.02539 https…

Distributed Iterative Hard Thresholding for Variable Selection in Tobit Models
While extensive research has been conducted on high-dimensional data and on regression with left-censored responses, simultaneously addressing these complexities remains challenging, with only a few proposed methods available. In this paper, we utilize the Iterative Hard Thresholding (IHT) algorithm on the Tobit model in such a setting. Theoretical analysis demonstrates that our estimator converges with a near-optimal minimax rate. Additionally, we extend the method to a distributed setting, re…

This https://arxiv.org/abs/2307.14642 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Linear Convergence of Black-Box Variational Inference: Should We Stick the Landing?
We prove that black-box variational inference (BBVI) with control variates, particularly the sticking-the-landing (STL) estimator, converges at a geometric (traditionally called "linear") rate under perfect variational family specification. In particular, we prove a quadratic bound on the gradient variance of the STL estimator, one which encompasses misspecified variational families. Combined with previous works on the quadratic variance condition, this directly implies convergence of BBVI with…

Fast Data-driven Greedy Sensor Selection for Ridge Regression
Yasuo Sasaki, Keigo Yamada, Takayuki Nagata, Yuji Saito, Taku Nonomura
https://arxiv.org/abs/2402.10596

Fast Data-driven Greedy Sensor Selection for Ridge Regression
We propose a data-driven sensor-selection algorithm for accurate estimation of the target variables from the selected measurements. The target variables are assumed to be estimated by a ridge-regression estimator which is trained based on the data. The proposed algorithm greedily selects sensors for minimization of the cost function of the estimator. Sensor selection which prevents the overfitting of the resulting estimator can be realized by setting a positive regularization parameter. The gre…

This https://arxiv.org/abs/2308.04916 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Heavy-tailed Bayesian nonparametric adaptation
We propose a new Bayesian strategy for adaptation to smoothness in nonparametric models based on heavy tailed series priors. We illustrate it in a variety of settings, showing in particular that the corresponding Bayesian posterior distributions achieve adaptive rates of contraction in the minimax sense (up to logarithmic factors) without the need to sample hyperparameters. Unlike many existing procedures, where a form of direct model (or estimator) selection is performed, the method can be see…

This https://arxiv.org/abs/2208.06039 has been replaced.
link: https://scholar.google.com/scholar?q=a

Semiparametric adaptive estimation under informative sampling
In survey sampling, survey data do not necessarily represent the target population, and the samples are often biased. However, information on the survey weights aids in the elimination of selection bias. The Horvitz-Thompson estimator is a well-known unbiased, consistent, and asymptotically normal estimator; however, it is not efficient. Thus, this study derives the semiparametric efficiency bound for various target parameters by considering the survey weight as a random variable and consequent…

On the Regret of Recursive Methods for Discrete-Time Adaptive Control with Matched Uncertainty
Aren Karapetyan, Efe C. Balta, Anastasios Tsiamis, Andrea Iannelli, John Lygeros
https://arxiv.org/abs/2404.02023

On the Regret of Recursive Methods for Discrete-Time Adaptive Control with Matched Uncertainty
Continuous-time adaptive controllers for systems with a matched uncertainty often comprise an online parameter estimator and a corresponding parameterized controller to cancel the uncertainty. However, such methods are often unimplementable, as they depend on an unobserved estimation error. We consider the equivalent discrete-time setting with a causal information structure. We propose a novel, online proximal point method-based adaptive controller, that under a weak persistence of excitation (…

This https://arxiv.org/abs/1612.06040 has been replaced.
link: https://scholar.google.com/scholar?q=a

Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels
We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the \emph{latent} block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants …

This https://arxiv.org/abs/2303.13281 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Uncertain Short-Run Restrictions and Statistically Identified Structural Vector Autoregressions
This study proposes a combination of a statistical identification approach with potentially invalid short-run zero restrictions. The estimator shrinks towards imposed restrictions and stops shrinkage when the data provide evidence against a restriction. Simulation results demonstrate how incorporating valid restrictions through the shrinkage approach enhances the accuracy of the statistically identified estimator and how the impact of invalid restrictions decreases with the sample size. The est…

This https://arxiv.org/abs/2202.12737 has been replaced.
link: https://scholar.google.com/scholar?q=a

Alpha-NML Universal Predictors
Inspired by the connection between classical regret measures employed in universal prediction and Rényi divergence, we introduce a new class of universal predictors that depend on a real parameter $α\geq 1$. This class interpolates two well-known predictors, the mixture estimators, that include the Laplace and the Krichevsky-Trofimov predictors, and the Normalized Maximum Likelihood (NML) estimator. We point out some advantages of this new class of predictors and study its benefits from two c…

Fast Data-driven Greedy Sensor Selection for Ridge Regression
Yasuo Sasaki, Keigo Yamada, Takayuki Nagata, Yuji Saito, Taku Nonomura
https://arxiv.org/abs/2402.10596

Fast Data-driven Greedy Sensor Selection for Ridge Regression
We propose a data-driven sensor-selection algorithm for accurate estimation of the target variables from the selected measurements. The target variables are assumed to be estimated by a ridge-regression estimator which is trained based on the data. The proposed algorithm greedily selects sensors for minimization of the cost function of the estimator. Sensor selection which prevents the overfitting of the resulting estimator can be realized by setting a positive regularization parameter. The gre…

This https://arxiv.org/abs/2305.15991 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finite sample rates for logistic regression with small noise or few samples
The logistic regression estimator is known to inflate the magnitude of its coefficients if the sample size $n$ is small, the dimension $p$ is (moderately) large or the signal-to-noise ratio $1/σ$ is large (probabilities of observing a label are close to 0 or 1). With this in mind, we study the logistic regression estimator with $p\ll n/\log n$, assuming Gaussian covariates and labels generated by the Gaussian link function, with a mild optimization constraint on the estimator's length to ensur…

This https://arxiv.org/abs/2402.00584 has been replaced.
link: https://scholar.google.com/scholar?q=a

Arellano-Bond LASSO Estimator for Dynamic Linear Panel Models
The Arellano-Bond estimator is a fundamental method for dynamic panel data models, which is widely used in practice. However, the estimator is severely biased when the data's time series dimension $T$ is long due to the large degree of overidentification. We propose a simple two-step approach to remove the bias. First, apply LASSO to the cross-section data at each time period to select the most informative moment conditions, using lagged values of suitable covariates. Second, apply a linear ins…

Koopman-based Deep Learning for Nonlinear System Estimation
Zexin Sun, Mingyu Chen, John Baillieul
https://arxiv.org/abs/2405.00627 https://

Koopman-based Deep Learning for Nonlinear System Estimation
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and invariably unmodeled dynamics present challenges in making precise predictions. In many cases the models exhibit extremely complicated behavior due to bifurcations and chaotic regimes. In this paper, we present a novel data-driven linear estimator that uses …

The modified conditional sum-of-squares estimator for fractionally integrated models
Mustafa R. K{\i}l{\i}n\c{c}, Michael Massmann
https://arxiv.org/abs/2404.12882

The modified conditional sum-of-squares estimator for fractionally integrated models
In this paper, we analyse the influence of estimating a constant term on the bias of the conditional sum-of-squares (CSS) estimator in a stationary or non-stationary type-II ARFIMA ($p_1$,$d$,$p_2$) model. We derive expressions for the estimator's bias and show that the leading term can be easily removed by a simple modification of the CSS objective function. We call this new estimator the modified conditional sum-of-squares (MCSS) estimator. We show theoretically and by means of Monte Carlo si…

On Ridge Estimation in High-dimensional Rotationally Sparse Linear Regression
Libin Liang, Zhiqiang Tan
https://arxiv.org/abs/2405.00974 https://

On Ridge Estimation in High-dimensional Rotationally Sparse Linear Regression
Recently, deep neural networks have been found to nearly interpolate training data but still generalize well in various applications. To help understand such a phenomenon, it has been of interest to analyze the ridge estimator and its interpolation limit in high-dimensional regression models. For this motivation, we study the ridge estimator in a rotationally sparse setting of high-dimensional linear regression, where the signal of a response is aligned with a small number, $d$, of covariates w…

This https://arxiv.org/abs/2401.10135 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Residual Based Error Estimator for Chemical-Mechanically Coupled Battery Active Particles
Adaptive finite element methods are a powerful tool to obtain numerical simulation results in a reasonable time. Due to complex chemical and mechanical couplings in lithium-ion batteries, numerical simulations are very helpful to investigate promising new battery active materials such as amorphous silicon featuring a higher energy density than graphite. Based on a thermodynamically consistent continuum model with large deformation and chemo-mechanically coupled approach, we compare three differ…

Quantile Outcome Adaptive Lasso: Covariate Selection for Inverse Probability Weighting Estimator of Quantile Treatment Effects
Takehiro Shoji, Jun Tsuchida, Hiroshi Yadohisa
https://arxiv.org/abs/2402.18185

Quantile Outcome Adaptive Lasso: Covariate Selection for Inverse Probability Weighting Estimator of Quantile Treatment Effects
When using the propensity score method to estimate the treatment effects, it is important to select the covariates to be included in the propensity score model. The inclusion of covariates unrelated to the outcome in the propensity score model led to bias and large variance in the estimator of treatment effects. Many data-driven covariate selection methods have been proposed for selecting covariates related to outcomes. However, most of them assume an average treatment effect estimation and may…

The modified conditional sum-of-squares estimator for fractionally integrated models
Mustafa R. K{\i}l{\i}n\c{c}, Michael Massmann
https://arxiv.org/abs/2404.12882

The modified conditional sum-of-squares estimator for fractionally integrated models
In this paper, we analyse the influence of estimating a constant term on the bias of the conditional sum-of-squares (CSS) estimator in a stationary or non-stationary type-II ARFIMA ($p_1$,$d$,$p_2$) model. We derive expressions for the estimator's bias and show that the leading term can be easily removed by a simple modification of the CSS objective function. We call this new estimator the modified conditional sum-of-squares (MCSS) estimator. We show theoretically and by means of Monte Carlo si…

This https://arxiv.org/abs/2403.01150 has been replaced.
link: https://scholar.google.com/scholar?q=a

Sequential Rotations and Error Analysis of a Simple Quaternion Estimator
Reference [1] introduces a novel closed-form quaternion estimator from two vector observations. The simplicity of the estimator sometimes yields singular expressions, the current annotation provides the simple rotation schemes for four singular cases. The estimator enables clear physical insights and a closed-form expression for the bias as a function of the quaternion error covariance matrix. The latter could be approximated up to second order with respect to the underlying measurement noise a…

Goal-oriented time adaptivity for port-Hamiltonian systems
Andreas Bartel, Manuel Schaller
https://arxiv.org/abs/2404.02641 https://a…

Goal-oriented time adaptivity for port-Hamiltonian systems
Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy balance in time discretizations, we propose an adaptive grid refinement technique based on a posteriori error estimation. The evaluation of the error estimator includes the computation of adjoint sensitivities. To interpret this adjoint equation as a backwards-…

This https://arxiv.org/abs/2311.06108 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonparametric consistency for maximum likelihood estimation and clustering based on mixtures of elliptically-symmetric distributions
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where $P$ is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separate…

Asymptotic Properties of the Distributional Synthetic Controls
Lu Zhang, Xiaomeng Zhang, Xinyu Zhang
https://arxiv.org/abs/2405.00953 https://

Asymptotic Properties of the Distributional Synthetic Controls
This paper enhances our comprehension of the Distributional Synthetic Control (DSC) proposed by Gunsilius (2023), focusing on its asymptotic properties. We first establish the DSC estimator's asymptotic optimality. The essence of this optimality lies in the treatment effect estimator given by DSC achieves the lowest possible squared prediction error among all potential treatment effect estimators that depend on an average of quantiles of control units. We also establish the convergence of the D…

Regularised Canonical Correlation Analysis: graphical lasso, biplots and beyond
Lennie Wells, Kumar Thurimella, Sergio Bacallado
https://arxiv.org/abs/2403.02979

Regularised Canonical Correlation Analysis: graphical lasso, biplots and beyond
Recent developments in regularized Canonical Correlation Analysis (CCA) promise powerful methods for high-dimensional, multiview data analysis. However, justifying the structural assumptions behind many popular approaches remains a challenge, and features of realistic biological datasets pose practical difficulties that are seldom discussed. We propose a novel CCA estimator rooted in an assumption of conditional independencies and based on the Graphical Lasso. Our method has desirable theoretic…

On a theory of martingales for censoring
Benjamin R. Baer, Robert L. Strawderman
https://arxiv.org/abs/2403.02840 https://arxiv.org/p…

On a theory of martingales for censoring
A theory of martingales for censoring is developed. The Doob-Meyer martingale is shown to be inadequate in general, and a repaired martingale is proposed with a non-predictable centering term. Associated martingale transforms, variation processes, and covariation processes are developed based on a measure of half-predictability that generalizes predictability. The development is applied to study the Kaplan Meier estimator.

Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator
Gilad Lerman, Feng Yu, Teng Zhang
https://arxiv.org/abs/2403.18658 https://

Theoretical Guarantees for the Subspace-Constrained Tyler's Estimator
This work analyzes the subspace-constrained Tyler's estimator (STE) designed for recovering a low-dimensional subspace within a dataset that may be highly corrupted with outliers. It assumes a weak inlier-outlier model and allows the fraction of inliers to be smaller than a fraction that leads to computational hardness of the robust subspace recovery problem. It shows that in this setting, if the initialization of STE, which is an iterative algorithm, satisfies a certain condition, then STE can…

A product-limit estimator of the conditional survival function when cure status is partially known
Wende C. Safari, Ignacio L\'opez-de-Ullibarri, M. Amalia J\'acome
https://arxiv.org/abs/2402.07022

A product-limit estimator of the conditional survival function when cure status is partially known
We introduce a nonparametric estimator of the conditional survival function in the mixture cure model for right censored data when cure status is partially known. The estimator is developed for the setting of a single continuous covariate but it can be extended to multiple covariates. It extends the estimator of Beran (1981), which ignores cure status information. We obtain an almost sure representation, from which the strong consistency and asymptotic normality of the estimator are derived. As…

This https://arxiv.org/abs/2305.17615 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Estimating overidentified linear models with heteroskedasticity and outliers
Overidentified two-stage least square (TSLS) is commonly adopted by applied economists to address endogeneity. Though it potentially gives more efficient or informative estimate, overidentification comes with a cost. The bias of TSLS is severe when the number of instruments is large. Hence, Jackknife Instrumental Variable Estimator (JIVE) has been proposed to reduce bias of overidentified TSLS. A conventional heuristic rule to assess the performance of TSLS and JIVE is approximate bias. This pa…

This https://arxiv.org/abs/2312.05985 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_eco…

Fused Extended Two-Way Fixed Effects for Difference-in-Differences with Staggered Adoptions
To address the bias of the canonical two-way fixed effects estimator for difference-in-differences under staggered adoptions, Wooldridge (2021) proposed the extended two-way fixed effects estimator, which adds many parameters. However, this reduces efficiency. Restricting some of these parameters to be equal (for example, subsequent treatment effects within a cohort) helps, but ad hoc restrictions may reintroduce bias. We propose a machine learning estimator with a single tuning parameter, fuse…

Positivity violations in marginal structural survival models with time-dependent confounding: a simulation study on IPTW-estimator performance
Marta Spreafico
https://arxiv.org/abs/2403.19606

Positivity violations in marginal structural survival models with time-dependent confounding: a simulation study on IPTW-estimator performance
In longitudinal observational studies, marginal structural models (MSMs) are a class of causal models used to analyze the effect of an exposure on the (survival) outcome of interest while accounting for exposure-affected time-dependent confounding. In the applied literature, inverse probability of treatment weighting (IPTW) has been widely adopted to estimate MSMs. An essential assumption for IPTW-based MSMs is the positivity assumption, which ensures that each individual in the population has …

Positivity violations in marginal structural survival models with time-dependent confounding: a simulation study on IPTW-estimator performance
Marta Spreafico
https://arxiv.org/abs/2403.19606

Positivity violations in marginal structural survival models with time-dependent confounding: a simulation study on IPTW-estimator performance
In longitudinal observational studies, marginal structural models (MSMs) are a class of causal models used to analyze the effect of an exposure on the (survival) outcome of interest while accounting for exposure-affected time-dependent confounding. In the applied literature, inverse probability of treatment weighting (IPTW) has been widely adopted to estimate MSMs. An essential assumption for IPTW-based MSMs is the positivity assumption, which ensures that each individual in the population has …

This https://arxiv.org/abs/2402.00584 has been replaced.
link: https://scholar.google.com/scholar?q=a

Arellano-Bond LASSO Estimator for Dynamic Linear Panel Models
The Arellano-Bond estimator is a fundamental method for dynamic panel data models, which is widely used in practice. However, the estimator is severely biased when the data's time series dimension $T$ is long due to the large degree of overidentification. We propose a simple two-step approach to remove the bias. First, apply LASSO to the cross-section data at each time period to select the most informative moment conditions, using lagged values of suitable covariates. Second, apply a linear ins…

A modified debiased inverse-variance weighted estimator in two-sample summary-data Mendelian randomization
Youpeng Su, Siqi Xu, Yilei Ma, Ping Yin, Wing Kam Fung, Peng Wang
https://arxiv.org/abs/2402.15086

A modified debiased inverse-variance weighted estimator in two-sample summary-data Mendelian randomization
Mendelian randomization uses genetic variants as instrumental variables to make causal inferences about the effects of modifiable risk factors on diseases from observational data. One of the major challenges in Mendelian randomization is that many genetic variants are only modestly or even weakly associated with the risk factor of interest, a setting known as many weak instruments. Many existing methods, such as the popular inverse-variance weighted (IVW) method, could be biased when the instru…

A Bayesian shrinkage estimator for transfer learning
Mohamed A. Abba, Jonathan P. Williams, Brian J. Reich
https://arxiv.org/abs/2403.17321 https://…

A Bayesian shrinkage estimator for transfer learning
Transfer learning (TL) has emerged as a powerful tool to supplement data collected for a target task with data collected for a related source task. The Bayesian framework is natural for TL because information from the source data can be incorporated in the prior distribution for the target data analysis. In this paper, we propose and study Bayesian TL methods for the normal-means problem and multiple linear regression. We propose two classes of prior distributions. The first class assumes the d…

This https://arxiv.org/abs/2206.08051 has been replaced.
link: https://scholar.google.com/scholar?q=a

Voronoi Density Estimator for High-Dimensional Data: Computation, Compactification and Convergence
The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because Voronoi cells rapidly increase in complexity as dimensions grow, making the necessary explicit computations infeasible. We define a variant of the VDE deemed Compactified Voronoi Density Estimator (CVDE), suitable for higher dimensions. We propose computationally e…

Double Robust Variance Estimation
Bonnie E. Shook-Sa, Paul N. Zivich, Chanhwa Lee, Keyi Xue, Rachael K. Ross, Jessie K. Edwards, Jeffrey S. A. Stringer, Stephen R. Cole
https://arxiv.org/abs/2404.16166

Double Robust Variance Estimation
Doubly robust estimators have gained popularity in the field of causal inference due to their ability to provide consistent point estimates when either an outcome or exposure model is correctly specified. However, the influence function based variance estimator frequently used with doubly robust estimators is only consistent when both the outcome and exposure models are correctly specified. Here, use of M-estimation and the empirical sandwich variance estimator for doubly robust point and varia…