Abstract

In this study, we explore a robust testing procedure for the high

dimensional location parameters testing problem. Initially, we introduce a spatialsign based max-type test statistic, which exhibits excellent performance for sparse

alternatives.

Subsequently, we demonstrate the asymptotic independence between this max-type test statistic and the spatial-sign based sum-type test statis-

tic (Feng and Sun, 2016). Building on this, we propose a spatial-sign based maxsum type testing procedure, which shows remarkable performance under varying

signal sparsity. Our simulation studies underscore the superior performance of

the procedures we propose.

Information

Preprint No.SS-2024-0051
Manuscript IDSS-2024-0051
Complete AuthorsJixuan Liu, Long Feng, Ping Zhao, Zhaojun Wang
Corresponding AuthorsLong Feng
Emailsflnankai@nankai.edu.cn

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Acknowledgments

The authors thank the editor, the associate editor and three anonymous

referees for helpful comments and discussions. This paper is partially supported by Shenzhen Wukong Investment Company, Tianjin Science Fund

for Outstanding Young Scholar (23JCJQJC00150), the Fundamental Research Funds for the Central Universities under Grant No. ZB22000105 and

63233075, the China National Key R&D Program (Grant Nos. 2019YFC1908502,

2022YFA1003703, 2022YFA1003802, 2022YFA1003803) and the National

Natural Science Foundation of China Grants (Nos. 12271271, 11925106,

12231011, 11931001 and 11971247).

Long Feng and Ping Zhao are the

Supplementary Materials

The online Supplementary Material provides the proofs of the lemmas, theorems given in Section 2-3 and two real data applications. The proofs for

lemmas and theorems are given in Appendix S1 and S2 respectively and

the real data applications are in Appendix S4, in the online Supplementary

Material.

Supplementary materials are available for download.