Stochastic difference equation approach to inference with missing data: Some new results

摘要

This paper is concerned with the study of the properties of the Stochastic EM estimator. The Stochastic EM estimator is an estimator derived from an iterative algorithm which handles statistical model with missing data. The first result we obtain is on the decomposition of a general stochastic difference equation underlying the Stochastic EM iterates into an additive form. Such decomposition allows a further analysis of the Markov chain underlying the Stochastic EM algorithm. The second result indicates that the Stochastic EM estimator differs from the maximum likelihood estimate by O (1/n ) where n is the sample size. It also shows that iterates derived from the additive stochastic difference equation converges to a normal distribution which is centered at the true value of the parameter as n (yields) (infinity).