High-Dimensional MANOVA Via Bootstrapping and Its Application to Functional and Sparse Count Data
提出一种通过自助法构造最大统计量的高维多元方差分析新方法，用于同时检验多个总体均值向量的相等性，适用于函数型数据和稀疏计数数据，并提供维度无关的收敛速度。
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.