The stochastic EM algorithm: Estimation and asymptotic results

The EM algorithm is a much used tool for maximum likelihood estimation in m issing or incomplete data problems. However, calculating the conditional ex pectation required in the E-step of the algorithm may be infeasible, especi ally when this expectation is a large sum or a high-dimensional integral. I nstead the expectation can be estimated by simulation. This is the common i dea in the stochastic EM algorithm and the Monte Carlo EM algorithm. In this paper some asymptotic results for the Stochastic EM algorithm are g iven, and estimation based on this algorithm is discussed. In particular, a symptotic equivalence of certain simple estimators is shown, and a simulati on experiment is carried out to investigate this equivalence in small and m oderate samples. Furthermore, some implementation issues and the possibilit y of allowing unidentified parameters in the algorithm are discussed.