Convergence of the iterative conditional estimation and application to mixture proportion identification

The iterative conditional estimation (ICE) is an iterative estimation method of the parameters in the case of incomplete data. Proposed since about fifteen years, ICE works under weak hypotheses and has been successfully applied in many unsupervised processing problems. In particular, it gave good results in unsupervised image segmentation based on complex models like hidden fuzzy Markov fields, hidden evidential Markov fields, or triplet Markov fields. However, there were no general theoretical results concerning its asymptotic behavior until now. The aim of this paper is to provide a general theorem, and to specify two applications: the mixture proportion estimation in a very general setting, and estimation of the components means in Gaussian mixture. The position of ICE with respect to the "Expectation-Maximization" (EM) method is also briefly discussed.