MAXIMUM-LIKELIHOOD-ESTIMATION FOR INCOMPLETE DATA

In this contribution, a stochastic algorithm, for maximum likelihood estimation is presented when the model of the complete data is exponential. This model encompasses the models of population mixture, deconvolution and source separation. It is shown that the asymptotically stable stationary points of the associated ODE correspond to the maxima of the incomplete likelihood. Conditions guaranteing the convergence of the stochastic algorithm to a stationary point of the likelihood are also presented. Finally it is demonstrated that the minima and the saddle-points of the likelihood are avoided almost surely.