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Distributions associated with the factors of Wilks' Λ in discriminant analysis

Published online by Cambridge University Press:  09 April 2009

A. M. Kshirsagar
A. M. Kshirsagar
Affiliation:
Southern Methodist University Dallas, Texas, U.S.A.
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Exact tests, based on factorization of Wilks' Λ were derived by Williams (1952, 1955) and Bartlett (1951), for testing the goodness of fit of a single hypothetical discriminant function, in the case of several groups. An analytical derivation of the distributions associated with these tests was given by the author (1964 a), after expressing the test statistics in canonical forms. Wilks' Λ to cover the case of s (s > 1) hypothetical discriminant functions. Radcliffe, in his paper, states that an analytical derivation of the distributions, as well as of the independence of the factors of Λ is desirable. This is done in the present paper, by expressing the test criteria in simpler forms and using matrix transformations in the multivariate Beta distribution (Kshirsager 1961). This is a straightforward extension of the author's paper (1964 a), which dealt with only one hypothetical discriminant function.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 3-4 , November 1969 , pp. 269 - 277
Copyright
Copyright © Australian Mathematical Society 1969

References

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