Estimation of Semiparametric Mixture Models Using an Empirical Likelihood-based Algorithm

• Activity Number: 420
• Type: Invited
• Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Yuichi Kitamura*+
• Companies: University of Pennsylvania
• Keywords: empirical likelihood ; mixture models ; EM algorithm ; semiparametric models ; nonparametric models ; unobserved heterogeneity

Abstract

(Finite) mixture models are useful in applied econometrics. They can be used to model unobserved heterogeneity, which plays major roles in labor economics, industrial organization, and other fields. Mixtures are also convenient in dealing with contaminated sampling models and models with multiple equilibria. Most of the currently available estimation methods for mixtures are entirely parametric, or at least they usually employ parametric component likelihood functions. This paper studies estimation of models with semiparametric component distributions. First, it presents some new nonparametric identification results. It is shown that mixture models are identified under very weak assumptions that are plausible in economic applications. Second, it proposes a method to estimate a mixture model treating its component distributions semiparametrically. It constructs an appropriate empirical likelihood function for the semiparametric model. While direct maximization of the empirical likelihood function for the model is impractical, an EM-type algorithm developed in the paper solves the difficulty. Some desirable properties of the new estimator are discussed.