Multivariate Two-Sided Tests for Normal Mean Vectors with Unknown Covariance Matrix

Abstract

In this study, we discuss two kinds of multivariate two-sided tests for normal mean vectors with unknown covariance matrix. First, assuming that all components of a normal mean vector are simultaneously nonnegative or non positive, we consider a multivariate two-sided test for testing whether the normal mean vector is equal to zero or not. Next, assuming that all differences of components between two normal mean vectors are simultaneously non negative or non positive, we consider a multivariate two-sided test for testing whether the two normal mean vectors are equal or not. We construct methods for testing by referring to Glimm et al. (2002), Tamhane and Logan (2002) and Sasabuchi (2007). Finally, we give some simulation results regarding critical values and power of the test intended to compare the three methods.

Keywords:

• β-distribution
• Orthogonal projection
• Power of the test

Mathematics Subject Classification:

• 62H15
• 62F30

Acknowledgments

The author is deeply grateful to the referees for their helpful advice and comments for revising the article. Special thanks are due to the editors and the associate editors for their constructive comments and suggestions. The author is also indebted to Dr. Tomohiro Nakamura for his useful advice regarding applications.