High-dimensional testing for proportional covariance matrices

JOURNAL OF MULTIVARIATE ANALYSIS

卷:171

Article

Tsukuda, Koji¹  Matsuura, Shun² 

[1] Univ Tokyo, Grad Sch Arts & Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538902, Japan

[2] Keio Univ, Fac Sci & Technol, Kohoku Ku, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan

关键词: Asymptotic test;    High-dimension;    Multivariate normal distribution;    Proportional covariance model;   

DOI  :  10.1016/j.jmva.2019.01.011

来源: Elsevier

【 摘 要 】

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 (sic) p (delta) for some delta is an element of (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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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