Sign-based Test for Mean Vector in High-dimensional and Sparse Settings  

作　　者：Wei LIU Ying Qiu LI 

机构地区：[1]College of Mathematics and Statistics,Hu'nan University of Finance and Economics,Changsha 410205,P.R.China [2]School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第1期93-108,共16页数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11571052);Social Science Research Foundation of Hu’nan Provincial Department(Grant No.15YBA066);Outstanding Youth Foundation of Hu’nan Provincial Department of Education(Grant No.17B047)

摘　　要：In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.

关 键 词：High-dimensional data maximum type test sign-based dense test sign-based sparsity test sum of squares type test testing mean vector 

分 类 号：O212.1[理学—概率论与数理统计]