New Tests for Multivariate Ordered Alternatives

Abstract

We consider testing the equality of vector means against a multivariate ordered alternative. An extension of the Abelson and Tukey test is first derived under the assumption that the covariance matrix is known. The asymptotic distribution is obtained when the covariance is estimated. We also extend Schaafsma and Smid's somewhere most powerful test to multivariate normal settings, under the assumption that the covariance matrix is known. An empirical power study shows that these tests perform better than their multi-sided χ² test counterparts.

Key Words:

• Multivariate normal distributions
• χ¯² Distribution
• Order restricted inference

Mathematics Subject Classification:

• Primary 62F03
• Secondary 62H15

Acknowledgment

This research was supported by grant KRF-99-003-D00060 of Korea Research Foundation.