Testing Regression Coefficients in High-Dimensional and Sparse Settings

作     者：Kai XU Yan TIAN Qing CHENG Kai XU;Yan TIAN;Qing CHENG

作者机构：School of Mathematics and StatisticsAnhui Normal UniversityWuhu 241002P.R.China Center for Quantitative MedicineDuke-NUS Medical SchoolNational University of SingaporeSingapore 169856 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2021年第37卷第10期

页      面：1513-1532页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 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）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11901006) the Natural Science Foundation of Anhui Province(Grant No.1908085QA06) the Talent Foundation of Anhui Normal University(Grant No.751811) 

主　　题：Extreme value distribution high-dimensional linear models maximum-type-test 

摘      要：In the high-dimensional setting,this article considers a canonical testing problem in multivariate analysis,namely testing coefficients in linear regression *** tests for highdimensional regression coefficients have been proposed in the recent ***,these tests are based on the sum of squares type statistics,that perform well under the dense alternatives and suffer from low power under the sparse *** order to attack this issue,we introduce a new test statistic which is based on the maximum type statistic and magnifies the sparse *** limiting null distribution of the test statistic is shown to be the extreme value distribution of type I and the power of the test is *** particular,it is shown theoretically and numerically that the test is powerful against sparse *** studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature.