Inference for high-dimensional linear expectile regression with de-biasing method

Xiang Li, Yu-Ning Li, Li-Xin Zhang and Jun Zhao

Computational Statistics & Data Analysis, 2024, vol. 198, issue C

Abstract: The methodology for the inference problem in high-dimensional linear expectile regression is developed. By transforming the expectile loss into a weighted-least-squares form and applying a de-biasing strategy, Wald-type tests for multiple constraints within a regularized framework are established. An estimator for the pseudo-inverse of the generalized Hessian matrix in high dimension is constructed using general amenable regularizers, including Lasso and SCAD, with its consistency demonstrated through a novel proof technique. Simulation studies and real data applications demonstrate the efficacy of the proposed test statistic in both homoscedastic and heteroscedastic scenarios.

Keywords: Amenable regularizer; De-biased Lasso; High-dimensional inference; Precision matrix estimation; Weighted least squares (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:198:y:2024:i:c:s0167947324000811

DOI: 10.1016/j.csda.2024.107997

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