Stochastic EM estimator in the presence of missing data - theory and applications

摘要

This thesis provides a study of a Monte Carlo version of the EM (for Expectation-Maximization) algorithm for handling complex missing-data structure in which high-dimensional integrations may be involved. Assuming a parametric model for the complete data, we propose a method for imputing values for missing data and then iteratively perform direct parametric inference based on the pseudo-complete data. If the iteration converges, the result of the procedure is a sample from a stationary distribution derived from the Markov chain formed by the iterations of the parameter. This algorithm is called Stochastic EM and the estimator we propose is the mean of the stationary distribution. Two examples are given, one from medical science and one from education to substantiate the theory. In the education example, the use of straightforward EM would require performing an overwhelmingly large number of high-dimensional numerical integrations even for a moderate sample of a thousand multivariate binary observations.