An approximate randomization test for the high-dimensional two-sample Behrens–Fisher problem under arbitrary covariances

Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays

Rui Wang and Wangli Xu

Biometrika, 2022, vol. 109, issue 4, 1117-1132

Abstract: SummaryThis paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of Chen & Qin (2010) is proposed. The asymptotic behaviour of the test statistic, as well as the randomized statistic, is studied under weak conditions. In our theoretical framework, observations are not assumed to be identically distributed even within groups. No condition on the eigenstructure of the covariance matrices is imposed. Furthermore, the sample sizes of the two groups are allowed to be unbalanced. Under general conditions, all possible asymptotic distributions of the test statistic are obtained. We derive the asymptotic level and local power of the approximate randomization test procedure. Our theoretical results show that the proposed test procedure can adapt to all possible asymptotic distributions of the test statistic, always has the correct test level asymptotically and has good power behaviour. Our numerical experiments show that the proposed test procedure has favourable performance compared with several alternative test procedures.

Keywords: Behrens–Fisher problem; High-dimensional data; Lindeberg principle; Randomization test (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:109:y:2022:i:4:p:1117-1132.

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