Projection-based High-dimensional Sign Test

作     者：Hui CHEN Chang Liang ZOU Run Ze LI Hui CHEN;Chang Liang ZOU;Run Ze LI

作者机构：School of Statistics and Data ScienceNankai UniversityTianjin 300071P.R.China Department of Statistics and Methodology CenterPennsylvania State University201 Old MainUniversity ParkPA 16802USA 

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

年 卷 期：2022年第38卷第4期

页      面：683-708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：NNSF of China Grants(Grant Nos.11925106,11690015,11931001 and 11971247) NSF of Tianjin Grant(Grant Nos.18JCJQJC46000 and 18ZXZNGX00140) 111 Project B20016 National Science Foundation(Grant Nos.DMS 1820702,DMS 1953196 and DMS 2015539) 

主　　题：High dimensional location test problem locally optimal test nonparametric test sample-splitting spatial sign test 

摘      要：This article is concerned with the high-dimensional location testing *** highdimensional settings,traditional multivariate-sign-based tests perform poorly or become infeasible since their Type I error rates are far away from nominal *** modifications have been proposed to address this challenging issue and shown to perform ***,most of modified sign-based tests abandon all the correlation information,and this results in power loss in certain *** propose a projection weighted sign test to utilize the correlation *** mild conditions,we derive the optimal direction and weights with which the proposed projection test possesses asymptotically and locally best power under *** from using the sample-splitting idea for estimating the optimal direction,the proposed test is able to retain type-I error rates pretty well with asymptotic distributions,while it can be also highly competitive in terms of *** advantage relative to existing methods is demonstrated in numerical simulations and a real data example.