High-Dimensional MANOVA Via Bootstrapping and Its Application to Functional and Sparse Count Data

• 成果类型: Article
• 署名作者: Lin, Zhenhua; Lopes, Miles E.; Muller, Hans-Georg
• 署名单位: National University of Singapore; University of California System; University of California Davis
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1920959
• 发表日期: 2023
• 页码: 177-191
• 关键词: one-way anova; 2-sample test; MULTIVARIATE-ANALYSIS; statistical inferences; linear-models; mean vectors; fruit-fly; variance; tests; EQUALITY

摘要

We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous confidence regions for the differences of population mean vectors. It is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a natural feature in relevant applications, we are able to provide dimension-free and nearly parametric convergence rates for Gaussian approximation, bootstrap approximation, and the size of the test. We demonstrate the proposed approach with ANOVA problems for functional data and sparse count data. The proposed methodology is shown to work well in simulations and several real data applications.