The Annals of Statistics
- Ann. Statist.
- Volume 31, Number 4 (2003), 1220-1259.
Convergence of the Monte Carlo expectation maximization for curved exponential families
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.
Ann. Statist. Volume 31, Number 4 (2003), 1220-1259.
First available in Project Euclid: 31 July 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 65C05: Monte Carlo methods 62-04: Explicit machine computation and programs (not the theory of computation or programming)
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Fort, Gersende; Moulines, Eric. Convergence of the Monte Carlo expectation maximization for curved exponential families. Ann. Statist. 31 (2003), no. 4, 1220--1259. doi:10.1214/aos/1059655912. https://projecteuclid.org/euclid.aos/1059655912