Central limit theorem for linear spectral statistics of large dimensional Kendall's rank correlation matrices and its applications

Zeng Li, Qinwen Wang, Runze Li

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. The statistical setting in this paper covers a wide range of highly skewed and heavy-tailed distributions since we do not require the components to be identically distributed, and do not need any moment conditions. We establish the central limit theorem (CLT) for the linear spectral statistics (LSS) of the Kendall's rank correlation matrices under the Marchenko-Pastur asymptotic regime, in which the dimension diverges to infinity proportionally with the sample size. We further propose three nonparametric procedures for high dimensional independent test and their limiting null distributions are derived by implementing this CLT. Our numerical comparisons demonstrate the robustness and superiority of our proposed test statistics under various mixed and heavy-tailed cases.

Original languageEnglish (US)
Pages (from-to)1569-1593
Number of pages25
JournalAnnals of Statistics
Volume49
Issue number3
DOIs
StatePublished - Jun 2021

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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