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Elliptically contoured model and factorization of wllks1 A
Authors:A. K. Gupta  D. G Kabe
Affiliation:1. Department of Mathematics and Statistics , Bowling Green State University , OH, Bowling Green, 43403-0221, USA;2. Department of Mathematics and Computer Science , St. Mary's University , Nova Scotia, Halifax, B3H3C3, Canada
Abstract:In a series of papers, Kshirsagar (1964, 1971) and McHenry and Kshirsagar (1977), factorize Wilks' A into a number of factors and find the independent null 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 independent or dependent variables. Essentially the factors of Wilks' A are the factors of certain multivariate beta distributed matrix or its determinant. The Bartlett decomposition of the underlying multivariate beta distribution into independent factors determines the distribution of these factors. The present paper generalizes Kshirsagar's (1971) normal theory to the elliptically contoured model, and shows that his results are null robust for the elliptically contoured model.
Keywords:Wilks' A factors  direction factors  collinearity factors  discriminant functions  canonical variables  goodness of fit tests  Bartlett decomposition  elliptically contoured model
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