2020/07/02 by Zhenhua Lin, Lin, Zhenhua, Miles E. Lopes +3 · 1 citation
Mathematics · #62G10 #62G20 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Random Matrices and Applications #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2007.01058
openalex publication_date 2020/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.