Semiparametric Modeling for Nonlinear Interactions

• Activity Number: 368
• Type: Invited
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Shujie Ma*+ and Peter Song
• Companies: University of California, Riverside and University of Michigan
• Keywords: B Splines ; interaction ; oracle property ; profile estimation ; semiparametric regression

Abstract

It has been a long history of utilizing interactions in regression analysis to investigate alterations in covariate-effects on response variables. In this paper we aim to address two kinds of new challenges resulted from the inclusion of such high-order effects in the regression model for complex data. The first kind arises from a situation where interaction effects of individual covariates are weak but those of combined covariates are strong, and the other kind pertains to the presence of nonlinear interactive effects directed by low-effect covariates. We propose a new class of semiparametric models with varying index coefficients, which enables us to model and assess nonlinear interaction effects between grouped covariates on the response variable. As a result, most of the existing semiparametric regression models are special cases of our proposed models. We develop a numerically stable and computationally fast estimation procedure utilizing both profile least squares method and local fitting. We establish both estimation consistency and asymptotic normality for the proposed estimators of index coefficients as well as the oracle property for the nonparametric function estimator.