Abstract

This paper is concerned with Spearman’s correlation matrices under large dimensional

regime, in which the data dimension diverges to infinity proportionally with the sample size. We establish the central limit theorem for the linear spectral statistics of Spearman’s correlation matrices,

which extends the results of Bao et al. (2015). We also study the improved Spearman’s correlation

matrices of Hoeffding (1948) which is a standard U-statistic of order 3. As applications, we propose

three new test statistics for large dimensional independent test and numerical studies demonstrate

the applicability of our proposed methods.

Information

Preprint No.SS-2024-0395
Manuscript IDSS-2024-0395
Complete AuthorsHantao Chen, Cheng Wang
Corresponding AuthorsCheng Wang
Emailschengwang@sjtu.edu.cn

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Acknowledgments

The authors thank the Editor, the Associate Editor, and anonymous reviewers for their

insightful comments on earlier versions of this paper. Cheng Wang’s research is partially

supported by NSFC 12031005, NSFC 72495121 and the fundamental research funds for

the central universities.

Supplementary Materials

The online Supplementary Material includes the detailed proofs of the main theorems and

additional lemmas.

Supplementary materials are available for download.