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Factorizations of the residual likelihood criterion in discriminant analysis

Published online by Cambridge University Press:  24 October 2008

J. Radcliffe
J. Radcliffe
Affiliation:
University CollegeLondon
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Extract

Certain exact tests were developed by Williams (1952) to deal with the goodness of fit of a single hypothetical discriminant function. Bartlett (1951) generalized these results by the use of the geometric method to any number of dependent and independent variables. Bartlett's paper is divided into two parts. The first deals with an approximate factorization of the residual likelihood criterion into an effect due to the difference between the hypothetical and sample functions, and an effect due to non-collinearity. A method is given for constructing confidence intervals from the first factor. The second part of the paper gives two possible exact factorizations of the likelihood criterion, expressing the results in terms of the sample canonical variables. Kshirsagar (1964a) has expressed these results in terms of the original variables and given an analytic proof of the distribution of the factors. Williams (1955, 1961) has outlined a generalization of these results to several discriminant functions and given the result for one of the possible factorizations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 4 , October 1966 , pp. 743 - 752
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

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