JSM 2005 Online Program

Abstract #304556

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Activity Number:	232
Type:	Contributed
Date/Time:	Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
Sponsor:	General Methodology
Abstract - #304556
Title:	L^2-Based Homogeneity Tests for Mixtures with Structural Parameters
Author(s):	Hongying Dai*+ and Richard Charnigo
Companies:	University of Kentucky and University of Kentucky
Address:	700 Woodland Avenue, Lexington, KY, 40508, United States
Keywords:	mixture distribution ; D-test statistic ; likelihood ratio test
Abstract:	How to ascertain the number of components in a mixture distribution from a standard parametric family with a single parameter has been thoroughly studied in numerous papers. However, a mixture distribution from a parametric family with both a parameter of central interest (e.g., a location parameter) and a structural parameter (e.g., a scale parameter) is often a more realistic model. In this work, we extend the D-test of Charnigo and Sun (2004) to such situations and characterize asymptotic properties of the D-test statistic. For example, in a partially constrained mixture reflecting contamination, the D-test statistic is shown to converge to 0 at the rate of n^{-1}. On the other hand, in a partially constrained mixture reflecting knowledge of the overall mean and variance, the D-test statistic is shown to converge at the rate of n^{-1/2}. The latter finding is in marked contrast to the behavior of the D-test statistic when there is no structural parameter. Simulation studies examine the performance of the D-test versus likelihood-ratio-based competitors, and the methodology is illustrated using data from a genetic disease study.

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