Optimization via simulation for maximum likelihood estimation in incomplete data models

Optimization via simulation is a promising approach for solving maximum likelihood problems in incomplete data models. Among the techniques proposed to date, the Monte-Carlo EM algorithm (MCEM) proposed by Wei and Tanner (1991) has a strong potential but very little is known on its behavior and on strategies for monitoring its convergence. In this contribution, the convergence of MCEM is investigated with a particular emphasis on the stability issue (which is not guaranteed in the original algorithm described by Wei and Tanner). A random truncation strategy, inspired by the Chen's truncation method for stochastic approximation algorithms, is proposed and analyzed. Finally, the application of our results to blind estimation problems in which the complete data likelihood is from the exponential family is discussed.