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 differences sample mean vectors. The proposed method proceeds construction simultaneous confidence regions for population It is suited simultaneously test equality several pairs vectors potentially more than two populations. By exploiting variance decay property natural feature in relevant applications, we are able provide dimension-free and nearly parametric convergence rates Gaussian approximation, bootstrap size test. demonstrate with problems functional data sparse count data. methodology shown work well simulations real applications.