Large dimensional Spearman's rank correlation matrices: The central limit theorem and its applications

TL;DR

This paper establishes a central limit theorem for Spearman's correlation matrices in high dimensions, extending previous results and proposing new test statistics for independence testing with demonstrated effectiveness.

Contribution

It extends the CLT to Spearman's correlation matrices in high dimensions and introduces new test statistics for independence testing.

Findings

CLT for Spearman's correlation matrices in large dimensions

Proposed three new test statistics for independence testing

Numerical studies confirm the effectiveness of the methods

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 [\emph{Ann. Statist.} 43(2015) 2588--2623]. We also study the improved Spearman's correlation matrices [\emph{Ann. Math. Statist} 19(1948) 293--325] 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.