A new maximum-type test for high-dimensional correlation matrices

Jing Chen, Ming Li, Kaige Zhao and Baisen Liu

Statistics & Probability Letters, 2025, vol. 220, issue C

Abstract: The exploration of the structure of high-dimensional correlation matrices has become an increasingly important topic in various fields. This paper aims to develop a novel method for testing the structure of high-dimensional correlation matrices. A new maximum-type test is proposed and the asymptotic distribution is derived, assuming that both the data dimension and the sample size tend towards infinity proportionally. Simulation studies show that our proposed test performs well for the sparse alternatives, dense alternatives, and a mixture of sparse and dense alternatives. Finally, the proposed method is employed to analyze a gene expression dataset.

Keywords: Correlation matrix; High-dimensional data; Hypothesis testing; Random matrix theory (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2025.110365

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