On Recursive Estimation in Incomplete Data Models

We consider a new recursive algorithm for parameter estimation from an independent incomplete data sequence. The algorithm can be viewed as a recursive version of the well-known EM algorithm, augmented with a Monte-Carlo step which restores the missing data. Based on recent results on stochastic algorithms, we give conditions for the a.s. convergence of the algorithm. Moreover, asymptotical variance of this estimator is reduced by a simple averaging. Application to finite mixtures is given with a simulation experiment.