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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 …

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, …

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…

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…