Rich Mixtures for Multidimensional Smoothing

• Activity Number: 130
• Type: Invited
• Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics*
• Author(s): David Scott*+ and Bill Szewczyk
• Affiliation(s): Rice University and Department of Defense
• Keywords: mixture models ; kernel estimators ; curse of dimensionality

Abstract

Mixture models, which include kernel estimators, are widely used to model complex densities; however, one is faced with the challenge of determining an appropriate number of components. Kernel methods are a special case of mixture models but are generally viewed as rather susceptible to the curse of dimensionality. Locally adaptive kernel estimators are highly desirable in multiple dimensions, but few practical algorithms exist for such estimation. Thus, mixture models may be viewed as a more parsimonious kernel estimator, but without trying to get the number of components exactly correct. In this talk, we describe how a mixture estimate may be calibrated by starting with a kernel estimator. The IPRA algorithm sequentially fits mixture models.