Penalized Least Squares for Single Index Models

• Activity Number: 157
• Type: Topic Contributed
• Date/Time: Monday, August 3, 2009 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Tao Huang*+ and Heng Peng
• Companies: University of Virginia and The Hong Kong Baptist University

Abstract

The single index model is a useful regression model for biometrics and econometrics. In this talk, we propose a nonconcave penalized least squares method to estimate both parameters and the link function of the single index model. Compared to other variable selection and estimation methods, the proposed method can estimate parameters and select variables simultaneously. Under some regularity conditions, we demonstrate that the proposed estimators have the so-called oracle property. Furthermore, we establish the asymptotic normality for the proposed estimators and develop a sandwich formula to estimate the standard deviations of the proposed estimators. The asymptotic results and the proposed sandwich formula are augmented by a simulation study and a real data analysis.