  Estimators derived from an EM algorithm are not robust since they are based
on the maximization of the likelihood function. We propose a proximal-point
algorithm based on the EM algorithm which aim to minimize a divergence
criterion. Resulting estimators are generally robust against outliers and
misspecification. An EM-type proximal-point algorithm is also introduced in
order to produce robust estimators for mixture models. Convergence properties
of the two algorithms are treated. We relax an identifiability condition
imposed on the proximal term in the literature; a condition which is generally
not fulfilled by mixture models. The convergence of the introduced algorithms
is discussed on a two-component Weibull mixture and a two-component Gaussian
mixture entailing a condition on the initialization of the EM algorithm in
order for the later to converge. Simulations on mixture models using different
statistical divergences are provided to confirm the validity of our work and
the robustness of the resulting estimators against outliers in comparison to
the EM algorithm.
