Asymptotic properties of the estimator for a finite mixture of exponential dispersion models

Abstract

This paper is concerned with a class of exponential dispersion distributions. We
particularly focused on the mixture models, which represent an extension of the
Gaussian distribution. It should be noted that, the parameters estimation of mix-
ture distributions is an important task in statistical processing. In order to estimate
the parameters vector, we proposed a formulation of the Expectation-Maximization
algorithm (EM) under exponential dispersion mixture distributions. Also, we devel-
oped a hybrid algorithm called Expectation-Maximization and Method of moments
algorithm (EMM). Under mild regularity, several convergence results of the EMM
algorithm were obtained. Through simulation studies, the robustness of the EMM
was proved and the strong consistency of the EMM sequence appeared when the
data set size and the number of iterations tend to infinity.