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arXiv · 2401.07267

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

Xiang Li·Yu-Ning Li·Li-Xin Zhang·Jun Zhao
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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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Xiang Li, Yu-Ning Li, Li-Xin Zhang, Jun Zhao. 2024-01-14. Inference for high-dimensional linear expectile regression with de-biased method. https://arxiv.org/abs/2401.07267

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