Semiparametric Mixtures of Regressions

• Activity Number: 122
• Type: Topic Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): David Hunter*+
• Companies: Penn State
• Keywords: Mixture models ; Semi-parametric mixtures

Abstract

Mixtures of regressions may be appropriate in cases where a response variable is thought to depend on one or more explanatory variables, but there exist different categories of explanatory-response pairs for which different regression relationships exist and we do not observe the category of each pair. Mixture-of-regressions models have appeared in the statistical literature, though not extensively and generally only in a fully parametric form. After a brief discussion of the parametric case (and its implementation in the mixtools package for R), we consider relaxing the parametric assumptions of a standard mixture of regressions in several directions: Allowing the error structure to be unspecified, allowing the regression curve to be unspecified, and allowing the mixing proportions to vary as a function of the predictors.