Union-Intersection Test for the Mean Vector When the Covariance Matrix is Totally Reducible

Abstract

The union-intersection test is derived for the mean vector of a multi-normal population when the covariance matrix is totally reducible. The performance of the test is compared to those of two other tests, the likelihood ratio test and a test discussed in Young (1976), using an information theory approach, by computing the small-sample powers through Monte Carlo techniques and also by computing the Pitman efficiency.

Key Words:

• Mean vector
• Roy's union-intersection test
• Pitman efficiency
• Totally reducible