A STOCHASTIC EM ALGORITHM FOR MIXTURES WITH CENSORED-DATA

The stochastic EM algorithm is a widely applicable approach for computing maximum likelihood estimates for the mixture problem. We present here an extension of the SEM algorithm in a particular case of incomplete data, where the loss of information is due both to mixture models and censored observations. We propose several solutions to implement the 'SEMcm algorithm' (SEM for censored mixture), showing in particular that one of these procedures solves numerical problems arising with the EMcm algorithm and mixtures of nonexponential-type distributions. Theoretically, we study the asymptotic behavior of SEMcm in the simple case of a two-component censored mixture, where the unknown parameter is the mixing proportion. We prove, for each SEMcm procedures, convergence of the stationary distribution to a Gaussian distribution located on the m.l.e. of the parameter. To conclude, we give some examples based on simulations for censored samples with a great amount of lost information.