Comparison of Five Tests for the Common Mean of Several Multivariate Normal Populations

Abstract

In this article, we evaluate the merits of some tests for testing about the common mean vector of several multivariate normal populations with different covariance matrices. Five tests, including the Fisher's exact test, are compared with respect to their powers. Powers are estimated using Monte Carlo simulation. Based on the comparison studies, we found that the Fisher's test and one of the test due to Zhou and Mathew [Zhou, L., Mathew, T. (1994). Combining independent tests in multivariate linear models. J. Multivariate Anal. 51:265–276] are in general more powerful than other three tests. The tests are illustrated using simulated data.

Key Words:

• Affine invariant
• Graybill–Deal estimator
• Hotelling T ² statistic
• Size
• Power

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62H15

Acknowledgment

The authors are thankful to a referee for providing valuable comments and suggestions.