Inferences in Simulation-Based Likelihood Using Importance Sampling

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Fassil Nebebe*+
• Companies: Concordia University
• Keywords: latent variables ; Monte Carlo methods ; multidimensional integration ; simulated maximum likelihood ; parameter dependent importance sampler

Abstract

Maximum likelihood estimation of parametric models with latent variables generally involves multidimensional integration which is often intractable. A popular approach under those circumstances has been the use of Monte Carlo methods for simulating the likelihood function numerically. It is well known that certain variance reduction methods, such as importance sampling, can greatly increase efficiency of computation. Further simplification is also possible with the use of "simulated maximum likelihood estimation". The use of importance sampling in simulated maximum likelihood estimation has been extensively studied in the literature along with the error variance in approximating the exact likelihood estimate conditional on the observed data values. Relatively less has been devoted to the study of inferences accommodating both sampling and Monte Carlo errors in the case of simulated maximum likelihood using importance sampling. We study both the simple and parameter dependent importance sampler. Both asymptotic and finite sampling properties are investigated. We consider more efficient methods in approximating finite sampling distributions using again simulation.