Nonlinear Varying Coefficient Models

• Activity Number: 297
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Esra Kurum*+ and Yang (Rick) Wang and Runze Li and Damla Senturk
• Companies: Penn State and Freddie Mac and Penn State and Penn State
• Keywords: Asymptotic normality ; Generalized Likelihood Tests ; Local linear regression ; Nonlinear regression model

Abstract

We extend varying coefficient models to nonlinear varying coefficient models, where the relationship between the predictors and the response variable is allowed to be nonlinear. We propose a local linear estimation technique for nonlinear varying coefficient models. Since there is no closed form for the resulting estimates in a nonlinear regression model, we propose additional Taylor's expansions to address the computational challenges arising in optimization. We establish asymptotic normality of the proposed estimators leading to point-wise asymptotic confidence bands for the targeted varying coefficient functions. An extension of the generalized likelihood ratio-type test is also proposed for testing whether the coefficient functions vary over a covariate. An application to an empirical ecological study and simulation studies are given to show the efficacy of the proposed method.