Asymptotic properties of a stochastic EM Algorithm for estimating mixing proportions
Jean Diebolt, Gilles Celeux · Stochastic Models · 1993
The purpose of this paper is to study the asymptotic behavior of the Stochastic EM algorithm (SEM) in a simple particular case within the mixture context. We consider the estimation of the mixing proportion p: of a two-component mixture of densities assumed to be known. We establish that as the sample size N tends to infinity, the stationary distribution of the ergodic Markov chain generated by SEM converges to a Gaussian distribution whose mean is the consistent maximum likelihood estimate of p:. The asymptotic variance is proportional to N -1