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

• 成果类型: Article
• 署名作者: Wang, Rui; Xu, Wangli
• 署名单位: Renmin University of China; Renmin University of China
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asac014
• 发表日期: 2022
• 页码: 11171132
• 关键词: Bootstrap; permutation; maxima; sums

摘要

This 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 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.