Preprint #97-22

Maximum Likelihood Estimation in Conditionally Specified Statistical Models

by

Jaehyung Lee and Mark S. Kaiser

We propose a strategy for maximum likelihood estimation of parameters appearing in the joint distribution of a set of random variables modeled through the specification of full conditional probability density or mass functions. This strategy relies on maximization of a sequence of Monte Carlo approximations to the log likelihood function. The fundamental issue addressed in our strategy is formation of an importance sampling distribution as a product of marginal functions, where those marginals are chosen in a way that reflects the influence of dependence on the first two moments of the actual statistical model under consideration. We also address a number of practical issue in the use of Monte Carlo methods to locate maximum likelihood estimates, including criteria for when an additional sampling distribution should be selected and the selection of appropriate starting values. The estimation strategy proposed is applied to a Winsorized Poisson auto-model to demonstrate the presence of positive spatial dependence in counts of an herbivorous mite.


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