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Title: High dimensional multiplier bootstrap tests with applications to MANOVA Authors:  Nilanjan Chakraborty - Michigan State University (United States) [presenting]
Abstract: The focus is on the Gaussian approximation of normalized sums of high dimensional random vectors over a class of convex sets. The class is flexible and general enough as it is defined through intersections of half-spaces and parametrized by a class of matrices. This newly proposed convex class helps us to quantify the effect of sparsity on the explicit convergence rate of the quality of the approximation. The resulting novel multiplier bootstrap method over this class allows conducting MANOVA tests for high-dimensional means. The resulting test is distribution- and correlation-free, and it can also be applied for Linear Hypothesis testing of means under a high-dimensional setup. The simulation studies for size and power conducted under different settings demonstrate the superiority of our approach over the available methods.