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Testing proportionality of two high-dimensional covariance matrices. (English) Zbl 1510.62244

Summary: 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.

MSC:

62H15 Hypothesis testing in multivariate analysis
62H10 Multivariate distribution of statistics
62E20 Asymptotic distribution theory in statistics
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

HDtest
PDFBibTeX XMLCite
Full Text: DOI

References:

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