Monte Carlo EM Estimation for Time Series Models Involving Counts
作者:
K.S. Chan,
Johannes Ledolter,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1995)
卷期:
Volume 90,
issue 429
页码: 242-252
ISSN:0162-1459
年代: 1995
DOI:10.1080/01621459.1995.10476508
出版商: Taylor & Francis Group
关键词: Asymptotic efficiency;Gibbs sampler;Latent process;Markov chain techniques;Parameter-driven models;Polio incidence series
数据来源: Taylor
摘要:
The observations in parameter-driven models for time series of counts are generated from latent unobservable processes that characterize the correlation structure. These models result in very complex likelihoods, and even the EM algorithm, which is usually well suited for problems of this type, involves high-dimensional integration. In this article we discuss a Monte Carlo EM (MCEM) algorithm that uses a Markov chain sampling technique in the calculation of the expectation in theEstep of the EM algorithm. We propose a stopping criterion for the algorithm and provide rules for selecting the appropriate Monte Carlo sample size. We show that under suitable regularity conditions, an MCEM algorithm will, with high probability, get close to a maximizer of the likelihood of the observed data. We also discuss the asymptotic efficiency of the procedure. We illustrate our Monte Carlo estimation method on a time series involving small counts: the polio incidence time series previously analyzed by Zeger.
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