Advances and Applications in Statistics
Volume 60, Issue 1, Pages 45 - 62
(January 2020) http://dx.doi.org/10.17654/AS060010045 |
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SIMULATED LIKELIHOOD ESTIMATION USING ITERATIVE IMPORTANCE SAMPLING
Tak K. Mak and Fassil Nebebe
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Abstract: Monte Carlo methods are popular alternatives to high dimensional numerical integration in maximum likelihood inference involving incomplete data or latent variables. It is well known that the efficiencies of Monte Carlo methods can be substantially increased by employing importance sampling. However, their efficiencies can be greatly compromised due to an inappropriate choice of an importance function. Traditionally, a normal based Laplace expansion has been used to approximate the locally optimal importance function. In this paper, we propose an alternative approach for selecting the importance function which is generally more efficient in the pointwise approximation of the likelihood function. Furthermore, the proposed importance sampler can also be conveniently simulated. The proposed choice of importance function is then applied to “multi-stage” simulated maximum likelihood estimation. It is shown that a modification to the simulated maximum likelihood estimate obtained leads to a very accurate approximation to the maximum likelihood estimate. Using a set of real data, the efficiencies of the proposed pointwise approximation to the likelihood and the simulated maximum likelihood procedure are demonstrated and compared with that of the normal based methods. |
Keywords and phrases: importance sampling, multiple integration, simulated likelihood, maximum likelihood estimation.
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