Affiliation:
1. Laboratory of Probability and Statistics, University of Sfax
Abstract
In this paper, we introduce finite mixture models with singular multivariate
normal components. These models are useful when the observed data involves
collinearities, that is when the covariance matrices are singular. They are
also useful when the covariance matrices are ill-conditioned. In the latter
case, the classical approaches may lead to numerical instabilities and give
inaccurate estimations. Hence, an extension of the Expectation Maximization
algorithm, with complete proof, is proposed to derive the maximum likelihood
estimators and cluster the data instances for mixtures of singular
multivariate normal distributions. The accuracy of the proposed algorithm is
then demonstrated on the grounds of several numerical experiments. Finally,
we discuss the application of the proposed distribution to financial asset
returns modeling and portfolio selection.
Publisher
National Library of Serbia
Cited by
2 articles.
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