Many-sample tests for the equality and the proportionality hypotheses between large covariance matrices

2024/09/10 by Tianxing Mei, Chen Wang, Mei, Tianxing +3
Mathematics · #FOS: Mathematics #Primary 62H15 #Random Matrices and Applications #Statistics Theory (math.ST) #secondary 62H10

paper · pdf · doi:10.48550/arxiv.2409.06296

openalex publication_date 2024/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper proposes procedures for testing the equality hypothesis and the proportionality hypothesis involving a large number of q covariance matrices of dimension p× p. Under a limiting scheme where p, q and the sample sizes from the q populations grow to infinity in a proper manner, the proposed test statistics are shown to be asymptotically normal. Simulation results show that finite sample properties of the test procedures are satisfactory under both the null and alternatives. As an application, we derive a test procedure for the Kronecker product covariance specification for transposable data. Empirical analysis of datasets from the Mouse Aging Project and the 1000 Genomes Project (phase 3) is also conducted.

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