Testing proportionality of two high-dimensional covariance matrices

Guanghui Cheng, Baisen Liu, Guoliang Tian and Shurong Zheng

Computational Statistics & Data Analysis, 2020, vol. 150, issue C

Abstract: This article proposes three tests for proportionality hypotheses regrading high-dimensional covariance matrices. Compared with currently available tests in the literature that fail in situations involving a “large p small n” or require knowledge of the underlying normal distributions, these tests are nonparametric, and do not require specifying any known distribution to derive asymptotic distributions under both the null hypothesis as well as an alternative hypothesis. The theoretical justification for the proposed tests is provided to ensure their validity, especially when the number of dimensions p is larger than the sample size n. Numerical studies show that the proposed tests are adaptively powerful against dense as well as sparse alternatives for a wide range of dimensions and sample sizes. The tests were used to analyze a gene expression dataset to verify their effectiveness.

Keywords: Covariance matrices; Dense alternatives; High-dimensional inference; Proportionality test; Sparse alternatives (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:150:y:2020:i:c:s0167947320300530

DOI: 10.1016/j.csda.2020.106962

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