Department of Mathematics , Beijing Normal University , Beijing, 100875, P.R.China
Abstract:
Suppose that ξ and η be two random vectors and that (ξτ, ητ have an elliptically contoured distribution or a multivariate normal distribution. In this article, we obtain some necessary and sufficient (N.S.) conditions such that the ratio of two quadratic forms, say ξτAξ and ητBη(for some symmetric nonnegative matrices A and B), has an F-distribution. As applications, we extend the classical F-test to some dependent two group samples. Two cases are considered: elliptically contoured and normal distributions.