Multi-sample hypothesis testing of high-dimensional mean vectors under covariance heterogeneity

Lixiu Wu () and Jiang Hu ()
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Lixiu Wu: Northeast Normal University
Jiang Hu: Northeast Normal University

Annals of the Institute of Statistical Mathematics, 2024, vol. 76, issue 4, No 2, 579-615

Abstract: Abstract In this paper, we focus on the hypothesis testing problem of the mean vectors of high-dimensional data in the multi-sample case. We propose two maximum-type statistics and apply a parametric bootstrap technique to compute the critical values. Unlike previous hypothesis testing methods that heavily depend on the structural assumptions of the unknown covariance matrix, the proposed methods accommodate a general covariance structure. Additionally, we introduce screening-based testing procedures to enhance the power of our tests. These test procedures do not require the use of approximate limiting distributions for the test statistics. Finally, we obtain and verify the theoretical properties through simulation studies.

Keywords: Multi-sample hypothesis; High dimension; Parametric bootstrap; Maximum-type statistics (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10463-024-00896-8

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