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

2024/01/14 by Xiang Li, Li Yu-ning, Li, Xiang +5
Computer Science · Engineering · Mathematics · #62F05 #62F12 #62J12 #Blind Source Separation Techniques #FOS: Computer and information sciences #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2401.07267

openalex publication_date 2024/01/14 · openalex created_date 2024/01/18 · openalex updated_date 2026/08/01

Abstract

In this paper, we address the inference problem in high-dimensional linear expectile regression. We transform the expectile loss into a weighted-least-squares form and apply a de-biased strategy to establish Wald-type tests for multiple constraints within a regularized framework. Simultaneously, we construct an estimator for the pseudo-inverse of the generalized Hessian matrix in high dimension with general amenable regularizers including Lasso and SCAD, and demonstrate its consistency through a new proof technique. We conduct simulation studies and real data applications to demonstrate the efficacy of our proposed test statistic in both homoscedastic and heteroscedastic scenarios.

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