Robust Estimation of Mixtures of Heavy-Tailed Distributions

• Activity Number: 635
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): A. M. Santos*+ and Karen Kafadar
• Companies: IBM/University of Colorado Denver and Indiana University
• Keywords: robustness ; finite mixtures ; EM algorithm ; biweight ; h-distribution

Abstract

We examine the robustness and efficiency of a variant of the EM algorithm for estimating parameters of mixtures of heavy-tailed distributions. Specifically, we use the biweight in an EM-like algorithm to estimate location, scale, and proportion of each component of a mixture of h-distributions. This family of long-tailed distributions, indexed by a tail-length parameter (h=0 corresponds to the Gaussian), provides a measure by which robustness and efficiency relative to the Gaussian can be assessed. We compare our results to those using the conventional EM-algorithm (in the context of a model that assumes Gaussian distributions, producing maximum likelihood estimates) and with Scott's L2E (2001) approach. Finally, we describe the application that motivated this research and our plans for future work.