Pointwise and functional approximations in Monte Carlo maximum likelihood estimation

作     者：Kuk, AYC Cheng, YW 

作者机构：Univ New S Wales Dept Stat Sydney NSW 2052 Australia 

出 版 物：《STATISTICS AND COMPUTING》 (统计学与计算)

年 卷 期：1999年第9卷第2期

页      面：91-99页

核心收录：

学科分类：0202[经济学-应用经济学] 02[经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Australian Research Council  ARC 

主　　题：EM algorithm Gibbs sampling hierarchical likelihood importance sampling marginal likelihood Newton Raphson procedure random effects 

摘      要：We consider the use of Monte Carlo methods to obtain maximum likelihood estimates for random effects models and distinguish between the pointwise and functional approaches. We explore the relationship between the two approaches and compare them with the EM algorithm. The functional approach is more ambitious but the approximation is local in nature which we demonstrate graphically using two simple examples. A remedy is to obtain successively better approximations of the relative likelihood function near the true maximum likelihood estimate. To save computing time, we use only one Newton iteration to approximate the maximiser of each Monte Carlo likelihood and show that this is equivalent to the pointwise approach. The procedure is applied to fit a latent process model to a set of polio incidence data. The paper ends by a comparison between the marginal likelihood and the recently proposed hierarchical likelihood which avoids integration altogether.