On a Flexible Information Criterion for Order Selection in Semiparametric Mixture Models

• Activity Number: 242
• Type: Invited
• Date/Time: Tuesday, August 9, 2005 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Richard Charnigo*+ and Ramani S. Pilla
• Companies: University of Kentucky and Case Western Reserve University

Abstract

Finite mixture models provide easily-interpreted representations of the heterogeneity in physical and biological phenomena; yet, they pose special challenges to statisticians, especially with regard to estimation of the order (i.e., the number of distinct components). Lindsay (1983) developed an elegant framework for nonparametric estimation of the mixing distribution (and, hence, of the order) in the absence of a structural parameter common to all components. However, under fairly general conditions, incorporation of a structural parameter results in nonexistence of the semiparametric estimate or in a degenerate semiparametric estimate. Thus, a different paradigm is required to accommodate the presence of a structural parameter. In this talk, we will propose a flexible information criterion (FLIC) by which both the order of a mixture model and the value of the structural parameter can be consistently estimated. The FLIC is adaptive in that the strength of the penalty is determined by the configuration of the data---a feature absent from the AIC and BIC. We also will investigate the performance of the FLIC through simulation experiments and applications to real data.