Simulated Likelihood Estimation of Measurement Error Models

• Activity Number: 526
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Fassil Nebebe*+
• Companies: Concordia University
• Keywords: importance sampling ; incidental parameters ; measurement error model ; polynomial functions ; simulated likelihood

Abstract

We consider in this paper a unified approach for the estimation of a general measurement error model. The model may contain incidental parameters, though they are assumed to be realizations of latent variables. In this sense, the model considered is "structural", but it differs from the traditional structural relationship in the uses of conditional analyses in the treatment of asymptotic inferences. Since the maximum likelihood function does not have a closed form, numerical methods for obtaining the maximum likelihood estimates are considered. In particular, the method of simulated likelihood based on importance sampling is studied in detail. It is seen that the procedure can be greatly facilitated with an automated choice of an importance function. Asymptotic properties of the simulated maximum likelihood estimates are investigated. The efficiency of the simulated likelihood approach is then compared with those of the traditional methods in the special case of polynomial functional relationships.