Automatic bias correction for testing in high-dimensional linear models

作     者：Zhou, Jing Claeskens, Gerda 

作者机构：Katholieke Univ Leuven ORStat Naamsestr 69 B-3000 Leuven Belgium Katholieke Univ Leuven Leuven Stat Res Ctr Naamsestr 69 B-3000 Leuven Belgium 

出 版 物：《STATISTICA NEERLANDICA》 (荷兰统计学)

年 卷 期：2023年第77卷第1期

页      面：71-98页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 

基　　金：Postdoc Fellowship of the Research Foundation Flanders KU Leuven internal fund [C16/20/002] Research Foundation-Flanders (FWO) Flemish Government Research Foundation Flanders 

主　　题：l(1)-regularization approximate message passing algorithm confidence interval high-dimensional linear model hypothesis testing loss function 

摘      要：Hypothesis testing is challenging due to the test statistic s complicated asymptotic distribution when it is based on a regularized estimator in high dimensions. We propose a robust testing framework for l-regularized M-estimators to cope with non-Gaussian distributed regression errors, using the robust approximate message passing algorithm. The proposed framework enjoys an automatically built-in bias correction and is applicable with general convex nondifferentiable loss functions which also allows inference when the focus is a conditional quantile instead of the mean of the response. The estimator compares numerically well with the debiased and desparsified approaches while using the least squares loss function. The use of the Huber loss function demonstrates that the proposed construction provides stable confidence intervals under different regression error distributions.