A Test for Multivariate Analysis of Variance in High Dimension

Abstract

In this article, we consider the problem of testing a general multivariate linear hypothesis in a multivariate linear model when the N × p observation matrix is normally distributed with unknown covariance matrix, and N ≤ p. This includes the case of testing the equality of several mean vectors. A test is proposed which is a generalized version of the two-sample test proposed by Srivastava and Du (2008). The asymptotic null and nonnull distributions are obtained. The performance of this test is compared, theoretically as well as numerically, with the corresponding generalized version of the two-sample Dempster (1958) test, or more appropriately Bai and Saranadasa (1996) test who gave its asymptotic version.

Keywords:

• Asymptotic distribution
• MANOVA
• Multivariate linear model
• Power comparison

2000 Mathematics Subject Classification:

• Primary 62H15
• Secondary 62F05

Acknowledgment

The authors would like to thank the referees for many comments and suggestions.