Abstract #301480

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JSM 2003 Abstract #301480
Activity Number: 24
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #301480
Title: Mixtures of Location-shifted Symmetric Distributions
Author(s): Shaoli Wang*+ and David R. Hunter and Thomas P. Hettmansperger
Companies: Pennsylvania State University and Pennsylvania State University and Pennsylvania State University
Address: 0325 Thomas Building, University Park, PA, 16802-2111,
Keywords: Hodges-Lehmann estimator ; identifiability ; nonparametric mixture
Abstract:

This paper considers a nonparametric approach to fitting mixture distributions that assumes only that the components are symmetric and come from the same location family. Unlike some other nonparametric treatments of mixtures in the literature, our approach assumes univariate rather than multivariate observations. We discuss sufficient conditions for the identifiability of these mixture models, completely classifying in a certain sense the identifiable models for the 2- and 3-component cases. We propose a new method for estimating the parameters in one of these identifiable mixture models and prove that it is strongly consistent. We also show that this estimator is essentially a generalization of the Hodges-Lehmann estimator of center for a symmetric distribution. Finally, we discuss the numerical aspects of implementing this estimation procedure in the 2-component case.

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