Novel multiplier bootstrap tests for high-dimensional data

Music City Center 

We propose to assess the quality of approximation of normalized sums by its Gaussian analogues over a new class of convex sets in a high-dimensional setup. This class allows to quantify the effect of sparsity on the convergence rate explicitly, which generalizes Chernozhukov et.al. (2017) results for hyper-rectangles and s-sparse convex sets. We also show that several of recent methods for tests of high-dimensional means are of the form of supremum of normalized sums over these new classes of convex sets. As application, we propose a new distribution and correlation free K-sample test of high-dimensional means (K>2) MANOVA, which non-trivially generalizes recent 2-sample test by Xue and Yao (2020). Finally, we also propose new tests of linear hypotheses in MANOVA. The tests are studied rigorously both theoretically and on simulations studies. They show very good performance in comparison to the existing methods in the literature.

high-dimensional testing

multiplier bootstrap

MANOVA 

Section on Nonparametric Statistics