Monte Carlo EM Estimation for Time Series Models Involving Counts
针对计数时间序列的参数驱动模型，提出一种蒙特卡罗EM算法，用马尔可夫链采样处理高维积分，并给出停止准则和样本量选择规则，适用于如脊髓灰质炎发病率等小计数序列。
Abstract 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 the E step 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.