Testing Equality of Two High-Dimensional Correlation Matrices

Abstract

This paper is concerned with testing the equality of two high-dimensional Pearson correlation matrices without any structural assumption under normal populations. A U-statistic based on the Frobenius norm of the difference between two transformational correlation matrices is proposed for testing the equality of two correlation matrices when both sample sizes and dimension tend to infinity. And the asymptotic normality of the proposed testing statistic is also derived under the null and alternative hypotheses. Moreover, the asymptotic power function is also presented. Simulation studies show that the proposed test performs very well in a wide range of settings and can be allowed for the case of large dimensions and small sample sizes.

Keywords

High dimension / Correlation matrices / U-statistics / Equality test / Asymptotic normality

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Funding

Natural Science Foundation of Guangdong Province (CN)(2018A030310068)

National Natural Science Foundation of China(11731015)

Science and Technology Program of GuangZhou, China(202102020368)

GuangDong Basic and Applied Basic Research Foundation(2019A1515110448)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature