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 mixture 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 developed 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.

An EM algorithm for singular Gaussian mixture models

“…In order to illustrate this procedure, as in the previous example 5.1, we considered 15 parameter sets for the mixture density (28) and generated for each set of parameters, 10 different random samples of size n = 3000. We, then, compared the estimates obtained using our suggested algorithm with projected data and the classical EM algorithm applied to the raw data.…”

“…When the studied model includes many classes, a mixture of non-singular normal distributions is used. These models were studied by many authors such as [5], [28], [19], [6] and [12]. They are increasingly used to model the distributions of diverse phenomena.…”

Lévy processes time-changed by the first-exit time of the inverse Gaussian subordinator

“…From statistical point of view, many papers have used the variance functions in order to estimate the parameters of exponential dispersion models, which are related to NEFs additively and reproductively. We may refer to [22], where variance function is used in order to give some asymptotic properties of the estimator for a finite mixture of exponential dispersion models and have applied the estimation results in the image segmentation. Furthermore, [5] have investigated the variance function of the Tweedie model for the modeling of the signal path loss prediction.…”