A stochastic approximation type EM algorithm for the mixture problem
- 1 October 1992
- journal article
- research article
- Published by Taylor & Francis in Stochastics and Stochastic Reports
- Vol. 41 (1-2) , 119-134
- https://doi.org/10.1080/17442509208833797
Abstract
The EM algorithm is a widely applicable approach for computing maximum likelihood estimates for incomplete data. We present a stochastic approximation type EM algorithm: SAEM. This algorithm is an adaptation of the stochastic EM algorithm (SEM) that we have previously developed. Like SEM, SAEM overcomes most of the well-known limitations of EM. Moreover, SAEM performs better for small samples. Furthermore, SAEM appears to be more tractable than SEM, since it provides almost sure convergence, while SEM provides convergence in distribution. Here, we restrict attention on the mixture problem. We state a theorem which asserts that each SAEM sequence converges a.s. to a local maximizer of the likelihood function. We close this paper with a comparative study, based on numerical simulations, of these three algorithms.Keywords
This publication has 5 references indexed in Scilit:
- A Fast Improvement to the Em Algorithm on its Own TermsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1989
- Mixture Densities, Maximum Likelihood and the EM AlgorithmSIAM Review, 1984
- On the Convergence Properties of the EM AlgorithmThe Annals of Statistics, 1983
- Finding the Observed Information Matrix When Using the EM AlgorithmJournal of the Royal Statistical Society Series B: Statistical Methodology, 1982
- Maximum Likelihood from Incomplete Data Via the EM AlgorithmJournal of the Royal Statistical Society Series B: Statistical Methodology, 1977