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August 2003 Convergence of the Monte Carlo expectation maximization for curved exponential families
Gersende Fort, Eric Moulines
Ann. Statist. 31(4): 1220-1259 (August 2003). DOI: 10.1214/aos/1059655912


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.


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Gersende Fort. Eric Moulines. "Convergence of the Monte Carlo expectation maximization for curved exponential families." Ann. Statist. 31 (4) 1220 - 1259, August 2003.


Published: August 2003
First available in Project Euclid: 31 July 2003

zbMATH: 1043.62015
MathSciNet: MR2001649
Digital Object Identifier: 10.1214/aos/1059655912

Primary: 62-04 , 65C05
Secondary: 60J10

Keywords: averaging procedure , EM algorithm , Metropolis Hastings algorithms , Monte Carlo EM Algorithm

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • August 2003
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