Minimum L2 Estimators for Poisson Mixtures with Two Components

• Activity Number: 233
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 12:00 PM to 1:50 PM
• Sponsor: General Methodology
• Author(s): Shuyi Shen*+ and Ian R. Harris
• Companies: Southern Methodist University and Southern Methodist University
• Keywords: divergence ; influence function ; L2 distance ; mixing proportions ; robustness

Abstract

Finite mixture model is extremely useful in fitting heterogeneous data. Often in practice, the primary interest in fitting a mixture model is to estimate the mixing proportions, while the component densities are already known or can be estimated separately from classified data. Current estimating methods used in the mixture problem include maximum likelihood, method of moments, minimum distance and Bayesian approaches. These methods typically give estimators for the mixing proportions that are not in explicit form and numerical methods are needed to calculate the estimate. A new minimum divergence estimator is developed and applied to estimation of Poisson mixtures with two components. The proposed estimator minimizes the integrated squared difference between densities or distributions (L2 distance). Unlike the other estimators, the proposed estimator for the mixing proportion is in closed form. The method also offers robust estimators while retaining acceptable efficiency compared to the MLE and the Minimum Hellinger Distance Estimator (MHDE). The application of the proposed method to epidemiological data will be presented.