A stochastic EM estimator in the presence of missing data - theory and applications
- Stanford Univ., CA (United States). Dept. of Statistics
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. We provide new theoretical results on the Stochastic EM estimator. First, under an exponential family setting, we show that asymptotically the Markov chain kernel of Stochastic EM can be decomposed into an additive stochastic difference equation. This decomposition allows us to provide useful results for the asymptotic behavior of the stationary distribution under specific conditions. The next result we obtain is that the Stochastic EM estimator is close to the maximum likelihood estimate. Another result shows that asymptotically the Stochastic EM iterations converge to a normal distribution with the true parameter as its mean. Bounds are obtained for the norm of the covariance matrix. There are two examples, 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.
- Research Organization:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 48618
- Report Number(s):
- SAND-95-8103; ON: DE95010329; TRN: 95:003812
- Resource Relation:
- Other Information: PBD: Apr 1995
- Country of Publication:
- United States
- Language:
- English
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