High-dimensional MANOVA via Bootstrapping and its Application to Functional Data 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, through constructing simultaneous confidence intervals for the differences of population mean vectors. The proposed procedure is able 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 naturally possessed in some 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 apply the method to ANOVA problems on functional data and sparse count data. Numerical studies via simulated and real data show that the proposed method has large power when the alternatives are not too dense, and also performs comparably when the alternatives are dense.