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

Xiang Li; Yu-Ning Li; Li Xin Zhang; Jun Zhao

doi:10.1016/j.csda.2024.107997

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

Xiang Li, Yu-Ning Li, Li Xin Zhang, Jun Zhao^*

^*Corresponding author for this work

The York Management School

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	107997
Number of pages	23
Journal	Computational Statistics & Data Analysis
Volume	198
Early online date	14 Jun 2024
DOIs	https://doi.org/10.1016/j.csda.2024.107997
Publication status	Published - 1 Oct 2024

Bibliographical note

Keywords

Amenable regularizer
De-biased Lasso
High-dimensional inference
Precision matrix estimation
Weighted least squares

Access to Document

10.1016/j.csda.2024.107997

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© 2024 Elsevier B.V. This is an author-produced version of the published paper. Uploaded in accordance with the University’s Research Publications and Open Access policy.
Accepted author manuscript, 784 KBLicence: CC BY

Cite this

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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.",

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