Tootfinder

Leveraging Covariates in Regression Discontinuity Designs
Matias D. Cattaneo, Filippo Palomba
https://arxiv.org/abs/2507.14311 https://

Leveraging Covariates in Regression Discontinuity Designs
It is common practice to incorporate additional covariates in empirical economics. In the context of Regression Discontinuity (RD) designs, covariate adjustment plays multiple roles, making it essential to understand its impact on analysis and conclusions. Typically implemented via local least squares regressions, covariate adjustment can serve three main distinct purposes: (i) improving the efficiency of RD average causal effect estimators, (ii) learning about heterogeneous RD policy effects, …

Generalisation and benign over-fitting for linear regression onto random functional covariates
Andrew Jones, Nick Whiteley
https://arxiv.org/abs/2508.13895 https://

Generalisation and benign over-fitting for linear regression onto random functional covariates
We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved locations, subject to additive noise. This leads us away from the standard assumption of i.i.d. data to a setting in which the $n$ covariate vectors are exchangeable but not independent in general. Under an assumption of independence across dimensions, $4$-th…

Correction of estimator bias in linear regression with categorical covariates with classification error
Alexandre Garcia Dias, Mariana Rodrigues Motta, Alexandre Hild Aono
https://arxiv.org/abs/2507.07245

Correction of estimator bias in linear regression with categorical covariates with classification error
The objective of this work is to propose an asymptotic correction method for the estimators of parameters from regression models with covariates subject to classification errors. A correction was developed based on the least squares estimators from regression with erroneous covariates, the marginal probability of the true covariates, and the conditional probability of the erroneous covariates given the true covariates. In this way, we can correct these estimators without the need to correct the…

Comparing Building Thermal Dynamics Models and Estimation Methods for Grid-Edge Applications
Ninad Gaikwad, Kunal Shankar, Anamika Dubey, Alan Love, Olvar Bergland
https://arxiv.org/abs/2508.09118

Comparing Building Thermal Dynamics Models and Estimation Methods for Grid-Edge Applications
We need computationally efficient and accurate building thermal dynamics models for use in grid-edge applications. This work evaluates two grey-box approaches for modeling building thermal dynamics: RC-network models and structured regression models. For RC-network models, we compare parameter estimation methods including Nonlinear Least Squares, Batch Estimation, and Maximum Likelihood Estimation. We use the Almon Lag Structure with Linear Least Squares for estimating the structured regression…

Counterfactual Survival Q Learning for Longitudinal Randomized Trials via Buckley James Boosting
Jeongjin Lee, Jong-Min Kim
https://arxiv.org/abs/2508.11060 https://

Counterfactual Survival Q Learning for Longitudinal Randomized Trials via Buckley James Boosting
We propose a Buckley James (BJ) Boost Q learning framework for estimating optimal dynamic treatment regimes under right censored survival data, tailored for longitudinal randomized clinical trial settings. The method integrates accelerated failure time models with iterative boosting techniques, including componentwise least squares and regression trees, within a counterfactual Q learning framework. By directly modeling conditional survival time, BJ Boost Q learning avoids the restrictive propor…

Estimating a regression function under possible heteroscedastic and heavy-tailed errors. Application to shape-restricted regression
Yannick Baraud, Guillaume Maillard
https://arxiv.org/abs/2506.00852

Estimating a regression function under possible heteroscedastic and heavy-tailed errors. Application to shape-restricted regression
We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a surrogate for the classical least squares estimator (LSE). For this new estimator, we establish a nonasymptotic risk bound with respect to the absolute loss which takes the form of an oracle type inequality. This inequality shows that our estimator possesses natural …

Demystifying Spectral Feature Learning for Instrumental Variable Regression
Dimitri Meunier, Antoine Moulin, Jakub Wornbard, Vladimir R. Kostic, Arthur Gretton
https://arxiv.org/abs/2506.10899

Demystifying Spectral Feature Learning for Instrumental Variable Regression
We address the problem of causal effect estimation in the presence of hidden confounders, using nonparametric instrumental variable (IV) regression. A leading strategy employs spectral features - that is, learned features spanning the top eigensubspaces of the operator linking treatments to instruments. We derive a generalization error bound for a two-stage least squares estimator based on spectral features, and gain insights into the method's performance and failure modes. We show that perform…

Semi-supervised learning for linear extremile regression
Rong Jiang, Keming Yu, Jiangfeng Wang
https://arxiv.org/abs/2507.01314 https://

Semi-supervised learning for linear extremile regression
Extremile regression, as a least squares analog of quantile regression, is potentially useful tool for modeling and understanding the extreme tails of a distribution. However, existing extremile regression methods, as nonparametric approaches, may face challenges in high-dimensional settings due to data sparsity, computational inefficiency, and the risk of overfitting. While linear regression serves as the foundation for many other statistical and machine learning models due to its simplicity, …

Sensitivity of weighted least squares estimators to omitted variables
Leonard Wainstein, Chad Hazlett
https://arxiv.org/abs/2508.02954 https://arxiv.org/pd…

Sensitivity of weighted least squares estimators to omitted variables
This paper introduces tools for assessing the sensitivity, to unobserved confounding, of a common estimator of the causal effect of a treatment on an outcome that employs weights: the weighted linear regression of the outcome on the treatment and observed covariates. We demonstrate through the omitted variable bias framework that the bias of this estimator is a function of two intuitive sensitivity parameters: (i) the proportion of weighted variance in the treatment that unobserved confounding …

Latent Variable Autoregression with Exogenous Inputs
Daniil Bargman
https://arxiv.org/abs/2506.04488 https://arxiv.org/pdf/2506.04488…

Latent Variable Autoregression with Exogenous Inputs
This paper introduces a new least squares regression methodology called (C)LARX: a (constrained) latent variable autoregressive model with exogenous inputs. Two additional contributions are made as a side effect: First, a new matrix operator is introduced for matrices and vectors with blocks along one dimension; Second, a new latent variable regression (LVR) framework is proposed for economics and finance. The empirical section examines how well the stock market predicts real economic activity …

High-Dimensional Matrix-Variate Diffusion Index Models for Time Series Forecasting
Zhiren Ma, Qian Zhao, Riquan Zhang, Zhaoxing Gao
https://arxiv.org/abs/2508.04259 https://

High-Dimensional Matrix-Variate Diffusion Index Models for Time Series Forecasting
This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $α$-PCA method to extract low-dimensional matrix factors and build a bilinear regression linking future outcomes to these factors, estimated via iterative least squares. To handle weak factor structures, we introduce a supervised screening step to select informative rows and columns. Theoretical properties, including consistency and asymptotic normality,…

Causal Inference in Panel Data with a Continuous Treatment
Zhiguo Xiao, Peikai Wu
https://arxiv.org/abs/2506.23226 https://arxiv.org/…

Causal Inference in Panel Data with a Continuous Treatment
This paper proposes a framework that incorporates the two-way fixed effects model as a special case to conduct causal inference with a continuous treatment. Treatments are allowed to change over time and potential outcomes are dependent on historical treatments. Regression models on potential outcomes, along with the sequentially conditional independence assumptions (SCIAs) are introduced to identify the treatment effects, which are measured by aggre causal responses. Least squares and generali…