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Abstract Details

Activity Number: 122
Type: Topic Contributed
Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #306958
Title: Regularization Approach to Nonparametric Estimation in Multivariate Mixtures
Author(s): Michael Levine*+ and David Hunter and Didier Chauveau
Companies: Purdue University and Penn State and Université d'Orléans
Address: 250 N. University St, West Lafayette , IN, 47907,
Keywords: nonparametric ; mixtures ; multivariate ; EM ; regularization ; ascent

Benaglia et al (2009) introduce an algorithm for nonparametric estimation of finite multivariate mixtures that resembles an EM algorithm. Conditional independence for coordinates of the random vectors is assumed. The algorithm works for any number of components and any dimensionality. However, this algorithm does not have an ascent property. Motivated by regularization argument of Eggermont and LaRiccia in their papers on the mixing density estimation in 1990's, we apply a similar approach to the problem of nonparametric estimation of finite mixtures. This algorithm possesses an ascent property and is a true EM algorithm. To the best of our knowledge, this is the first true EM algorithm that can fit a mixture of an arbitrary number of multivariate nonparametric components. Extensive simulations demonstrate an excellent performance of the new algorithm in a variety of situations.

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