Novel multiplier bootstrap tests for high-dimensional data with applications to MANOVA

Abstract

New bootstrap tests are proposed for linear hypotheses testing of high-dimensional means. In particular, they handle multiple-sample one- and two-way MANOVA tests with unequal cell sizes and unequal unknown cell covariances, as well as contrast tests in elegant and unified way. New tests are compared theoretically and on simulations studies with existing popular contemporary tests. They enjoy consistency, computational efficiency, very mild moment/tail conditions. They avoid the estimation of correlation or precision matrices, and allow the dimension to grow with sample size exponentially. Additionally, they allow the number of groups and the sparsity to grow with the sample size exponentially, thus broadening their applicability.