Test for high-dimensional mean vectors via the weighted L₂-norm

2024/01/30 by Li, Jianghao, Niu, Zhenzhen, Hong, Shizhe +1
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2401.17143

Abstract

In this paper, we propose a novel approach to test the equality of high-dimensional mean vectors of several populations via the weighted L₂-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 in weakly dense cases when the nonzero signal in mean vectors is present. Furthermore, we compare the proposed test with existing tests using simulation results, demonstrating that the weighted L₂-norm-based test statistic exhibits favorable properties in terms of both size and power.

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