Test for High-Dimensional Mean Vectors via the Weighted L₂-norm

Abstract

In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted

L_2

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-norm. We establish the asymptotic normality of the test statistics under the null hypothesis. We also explain theoretically why our test statistics can be highly useful when the nonzero signal in mean vectors is weakly dense with almost the same sign. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the weighted

L_2

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-norm-based test statistic exhibits favorable properties in terms of both size and power.

Keywords

High-dimensional data / Mean vector tests / U-statistics / 62H15 / 62E20

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Funding

National Natural Science Foundation of China(12271536)

RIGHTS & PERMISSIONS

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