A one-way MANOVA test for high-dimensional data using clustering subspaces

Abstract

This study focuses on the high-dimensional one-way analysis of variance problem, specifically, testing whether multiple population mean vectors are equal in the context of high-dimensional data. To solve the problem that classical multivariate analysis of variance (MANOVA) test statistics are undefined when the dimensionality surpasses the sample size, we propose a random permutation test using low-dimensional subspaces obtained by clustering of variables. The test statistics are derived from a one-way MANOVA decomposition for clustered variables and this approach utilizes the correlation information among variables to ensure high testing power. Simulation studies indicate that the proposed test performs well with high-dimensional data.