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High-dimensional testing for proportional covariance matrices

Koji Tsukuda and Shun Matsuura

Journal of Multivariate Analysis, 2019, vol. 171, issue C, 412-420

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≍pδ 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.

Keywords: Asymptotic test; High-dimension; Multivariate normal distribution; Proportional covariance model (search for similar items in EconPapers)
Date: 2019
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