High-dimensional MANOVA via Bootstrapping and its Application to Functional and Sparse Count Data

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.

我们提出了一种基于含样本均值向量差的自助法最大统计量的高维多元方差分析（Multivariate ANOVA）新方法。所提方法通过构建总体均值向量差的同时置信区域来开展求解，可同时检验潜在多于两个总体的多组均值向量对的相等性。借助相关应用中天然存在的方差衰减特性，我们可为高斯近似、自助法近似以及检验的显著性水平提供维度无关且近参数的收敛速率。我们通过函数型数据与稀疏计数数据的方差分析（ANOVA）问题对所提方法进行了实证验证，实验结果表明，该方法在模拟实验与多项实际数据应用中均表现出色。