# Pointwise and functional approximations in Monte Carlo maximum likelihood estimation

@article{Kuk1999PointwiseAF, title={Pointwise and functional approximations in Monte Carlo maximum likelihood estimation}, author={Anthony Y. C. Kuk and Yuk W. Cheng}, journal={Statistics and Computing}, year={1999}, volume={9}, pages={91-99} }

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… Expand

#### 33 Citations

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For smaller samples, this work proposes to use the current posterior as the next prior distribution to make the posterior simulations closer to the maximum likelihood estimate (MLE) and hence improve the likelihood approximation. Expand

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Fitting of non-Gaussian hierarchical random effects models by approximate maximum likelihood can be made automatic to the same extent that Bayesian model fitting can be automated by the program BUGS.… Expand

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Generalized linear mixed models have become a popular choice for modeling correlated and non-normal response data, with an increasing number of methods available for fitting these models. However,… Expand

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