On wilks' a factorization noncentral distribution theory

Abstract

Kshirsagar in a series of papers, see e.g., Kshirsagar (1964), (1971), (1972), McHenry and Kshirsagar (1977), factorizes Wilks A into a number of factors and finds the independent central multivariate beta densities of these factors. These factors are the likelihood ratio test criteria for testing the goodness of fit of certain assigned discriminant functions or canonical variables either in the space of dependent or independent variables. Essentially the factors of Wilks A are the factors of a certain multivariate beta distributed matrix or its determinant. The Bartlett decomposition of the underlying multivariate beta distribution into independent factors determines the distributions of these factors. In the noncentral case the distributions of these factors are not independent. However, the marginal noncentral distribution of each factor can be obtained. The present paper studies a typical paper of Kshirsagar's (1971), and generalizes Kshirsagar's Wilks A factorization central distribution theory to th...