A High-Dimensional Test for Multivariate Analysis of Variance Under a Low-Dimensional Factor Structure

Abstract

In this paper, the problem of high-dimensional multivariate analysis of variance is investigated under a low-dimensional factor structure which violates some vital assumptions on covariance matrix in some existing literature. We propose a new test and derive that the asymptotic distribution of the test statistic is a weighted distribution of chi-squares of 1 degree of freedom under the null hypothesis and mild conditions. We provide numerical studies on both sizes and powers to illustrate performance of the proposed test.

Keywords

High-dimensional data / MANOVA / Low-dimensional factor structure / Chi-square distribution

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Funding

National Natural Science Foundation of China(11601008)

Anhui Normal University(2016XJJ101)

Natural Science Foundation of Anhui Province(1508085QA11)