# High-dimensional testing for proportional covariance matrices

Koji Tsukuda, Shun Matsuura

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

## Abstract

Hypothesis testing for the proportionality of covariance matrices is a classical statistical problem and has been widely studied in the literature. However, there have been few treatments of this test in high-dimensional settings, especially for the case where the number of variables is larger than the sample size, despite high-dimensional statistical inference having recently received considerable attention. This paper studies hypothesis testing for the proportionality of two covariance matrices in the high-dimensional setting: m,n≍p δ for some δ∈(1∕2,1), where m and n denote the sample sizes and p denotes the number of variables. A test statistic is proposed and its asymptotic distribution is derived under multivariate normality. The non-asymptotic performance of the proposed test procedure is numerically examined.

Original language English 412-420 9 Journal of Multivariate Analysis 171 https://doi.org/10.1016/j.jmva.2019.01.011 Published - May 2019 Yes

## All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Numerical Analysis
• Statistics, Probability and Uncertainty
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