Efficient simulated maximum likelihood estimation through explicitly parameter dependent importance sampling

Abstract

There exists an overall negative assessment of the performance of the simulated maximum likelihood algorithm in the statistics literature, founded on both theoretical and empirical results. At the same time, there also exist a number of highly successful applications. This paper explains the negative assessment by the coupling of the algorithm with “simple importance samplers”, samplers that are not explicitly parameter dependent. The successful applications in the literature are based on explicitly parameter dependent importance samplers. Simple importance samplers may efficiently simulate the likelihood function value, but fail to efficiently simulate the score function, which is the key to efficient simulated maximum likelihood. The theoretical points are illustrated by applying Laplace importance sampling in both variants to the classic salamander mating model.