Convergence of the Monte Carlo expectation maximization for curved exponential families
Open Access
- 1 August 2003
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 31 (4) , 1220-1259
- https://doi.org/10.1214/aos/1059655912
Abstract
The Monte Carlo expectation maximization (MCEM) algorithm is a versatile tool for inference in incomplete data models, especially when used in combination with Markov chain Monte Carlo simulation methods. In this contribution, the almost-sure convergence of the MCEM algorithm is established. It is shown, using uniform versions of ergodic theorems for Markov chains, that MCEM converges under weak conditions on the simulation kernel. Practical illustrations are presented, using a hybrid random walk Metropolis Hastings sampler and an independence sampler. The rate of convergence is studied, showing the impact of the simulation schedule on the fluctuation of the parameter estimate at the convergence. A novel averaging procedure is then proposed to reduce the simulation variance and increase the rate of convergence.Keywords
This publication has 25 references indexed in Scilit:
- On the geometric ergodicity of hybrid samplersJournal of Applied Probability, 2003
- Conditions for convergence of Monte Carlo EM sequences with an application to product diffusion modelingThe Econometrics Journal, 1999
- Maximum Likelihood Estimation for Probit-Linear Mixed Models with Correlated Random EffectsPublished by JSTOR ,1997
- Fitting Full-Information Item Factor Models and an Empirical Investigation of Bridge SamplingJournal of the American Statistical Association, 1996
- Random perturbations of recursive sequences with an application to an epidemic modelJournal of Applied Probability, 1995
- Monte Carlo EM Estimation for Time Series Models Involving CountsJournal of the American Statistical Association, 1995
- Estimation of innovation diffusion models with application to a consumer durableMarketing Letters, 1995
- A stochastic approximation type EM algorithm for the mixture problemStochastics and Stochastic Reports, 1992
- A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation AlgorithmsJournal of the American Statistical Association, 1990
- On the Convergence Properties of the EM AlgorithmThe Annals of Statistics, 1983