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Abstract Details

Activity Number: 642
Type: Topic Contributed
Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #304771
Title: Large-Sample Convergence of the Nonparametric Density Mixture Estimators
Author(s): Michael Levine*+ and David Hunter
Companies: Purdue University and Penn State University
Address: Dept.of Statistics, HAAS Bldg, West Lafayette, IN, 47907-2066, United States
Keywords: nonparametric ; mixture ; conditional independence ; Em-type algorithm
Abstract:

Estimation of the nonparametric multivariate density mixtures is a relatively new area of research in mathematical statistics. Commonly, conditional independence for coordinates of the random vectors is assumed; such an assumption can be thought of as an extension of the independence assumption for longitudinal data where it is routinely assumed to be conditional upon the subject. A number of algorithms that can be used to estimate both weights and functional components in such a mixture has been recently suggested. While the empirical performance of these algorithms seems to be fairly impressive, their large sample properties have been almost completely unknown until now. In this presentation, we will present some of our recent results concerning asymptotic large-sample behavior for one such algorithm. The algorithm in question is an EM-type algorithm that maximizes the explicit objective function. This last fact turns out to be decisive in establishing the asymptotic properties of our algorithm.


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