Selection of Consistent Roots to the Likelihood Equation in Finite Mixtures of Location-Scale Distributions

• Activity Number: 459
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Byungtae Seo and Daeyoung Kim*+
• Companies: Texas Tech University and University of Massachusetts, Amherst
• Keywords: Consistency ; Normal mixture ; Spurious maximizer ; Unbounded likelihood

Abstract

Finite mixtures of location-scale distributions such as normal mixture distributions are attractive in capturing any nonnormal features in the data caused by underlying group structure. However, it is well known that the maximum likelihood estimation in the location-scale mixture distributions is problematic due to the unbounded likelihood and the existence of multiple roots to the likelihood equation including a so-called spurious root. In this article we propose a new method designed to avoid such singularities and spurious local maximizers in the mixture likelihood. We show that our proposed methodology can choose a root with a desirable asymptotic property among all found roots to the likelihood equation. We illustrate the implementation of the proposed methodology through several examples and simulation study.