JSM 2004 - Toronto

Abstract #301016

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Activity Number: 53
Type: Contributed
Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
Sponsor: General Methodology
Abstract - #301016
Title: A Mixture Model Using Poisson Kernel Components
Author(s): Ke Yang*+ and Bruce G. Lindsay
Companies: Pennsylvania State University and Pennsylvania State University
Address: 422A Thomas Bldg., University Park, PA, 16802,
Keywords: Poisson kernel ; EM algorithm ; mixture model ; nonparametric MLE ; directional data
Abstract:

The Poisson kernel originated from a famous Dirichlet problem. As a probability density function, it can be used to describe the distribution of directional data. The simplest Poisson kernel distribution is the univariate Poisson kernel distribution on a circle, which is well known as wrapped Cauchy distribution. Maximum likelihood estimation for the wrapped Cauchy distribution was studied by Kent and Tyler (1988). We extend their result to higher dimensions and construct an EM algorithm for the MLE. Then we consider the mixture model with the Poisson kernel used as the component density. We discuss the identifiability of the mixture model and its nonparametric MLE. This mixture model can be applied to directional data or normalized data, such as normalized microarray data.

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