Maximum Likelihood Estimators and Likelihood Ratio Criteria for Multivariate Elliptically Contoured Distributions

Abstract
In this paper we generalize the theory of maximum likelihood estimation and likelihood ratio criteria from normal distributions to multivariate elliptically contoured distributions for which the vector observations are not necessarily either normal or independent. We find that many usual likelihood ratio criteria and their null distributions are the same in the class of multivariate elliptically contoured distributions.

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