A stochastic approximation type EM algorithm for the mixture problem

Abstract

The EM algorithm is a widely applicable approach for computing maximum likelihood estimates for incomplete data. We present a stochastic approximation type EM algorithm: SAEM. This algorithm is an adaptation of the stochastic EM algorithm (SEM) that we have previously developed. Like SEM, SAEM overcomes most of the well-known limitations of EM. Moreover, SAEM performs better for small samples. Furthermore, SAEM appears to be more tractable than SEM, since it provides almost sure convergence, while SEM provides convergence in distribution. Here, we restrict attention on the mixture problem. We state a theorem which asserts that each SAEM sequence converges a.s. to a local maximizer of the likelihood function. We close this paper with a comparative study, based on numerical simulations, of these three algorithms.