Convergence of the Monte Carlo expectation maximization for curved exponential families

• 成果类型: Article
• 署名作者: Fort, G; Moulines, E
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2003
• 页码: 1220-1259
• 关键词: em algorithm; maximum-likelihood; Stochastic algorithms; time-series; models; counts

摘要

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.