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Estimators derived from an EM algorithm are not robust since they are basedon the maximization of the likelihood function. We propose a proximal-pointalgorithm based on the EM algorithm which aim to minimize a divergencecriterion. Resulting estimators are generally robust against outliers andmisspecification. An EM-type proximal-point algorithm is also introduced inorder to produce robust estimators for mixture models. Convergence propertiesof the two algorithms are treated. We relax an identifiability conditionimposed on the proximal term in the literature; a condition which is generallynot fulfilled by mixture models. The convergence of the introduced algorithmsis discussed on a two-component Weibull mixture and a two-component Gaussianmixture entailing a condition on the initialization of the EM algorithm inorder for the later to converge. Simulations on mixture models using differentstatistical divergences are provided to confirm the validity of our work andthe robustness of the resulting estimators against outliers in comparison tothe EM algorithm.

Two Iterative Proximal-Point Algorithms for the Calculus of Divergence-based Estimators with Application to Mixture Models