On Semiparametric Exponential Tilt Regression Models

• Activity Number: 424
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Alan Huang*+ and Paul J. Rathouz
• Companies: The University of Chicago and The University of Chicago
• Keywords: exponential tilting ; semiparametric model ; likelihood ratio test ; generalized linear models

Abstract

A semiparametric exponential tilt regression model was introduced by Rathouz & Gao (2009) as a semiparametric generalization of generalized linear models (see, e.g., McCullagh & Nelder, 1989). This approach differs from quasi-likelihood (Wedderburn, 1974) in that it treats the error distribution as a completely unspecified infinite-dimensional parameter in the likelihood function. I will present conditions under which profiling out the error distribution in the likelihood function results in a profile likelihood that behaves asymptotically like the true likelihood for the parameters in the mean model, thereby obtaining asymptotically normal estimators for mean parameters that are also asymptotically efficient. I will also comment on how inferences can be made on the nonparametric component.