Inference concerning the Mean Vector When the Covariance Matrix is Totally Reducible

Abstract

Given a random sample from a p-variate normal distribution , the likelihood ratio criterion and an information theory criterion, which is an analogue of Hotelling's T ², are given for testing (known) under the condition that Σ is totally reducible, that is, diagonalizable by an orthogonal matrix which depends upon the pattern but not on the unknown elements of Σ. Exact, approximate and asymptotic distributions of the test criteria are considered and various confidence regions concerning are provided. Application to repeated measures experiments is discussed.