Convergence of the Monte Carlo expectation maximization for curved exponential families
Gersende Fort and Eric Moulines
Source: Ann. Statist. Volume 31, Number 4
(2003), 1220-1259.
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.
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Keywords: EM algorithm; Monte Carlo EM algorithm; Metropolis Hastings algorithms; averaging procedure
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1059655912
Digital Object Identifier: doi:10.1214/aos/1059655912
Mathematical Reviews number (MathSciNet): MR2001649
Zentralblatt MATH identifier: 02077798
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