Model Selection and Model Averaging Partially Linear Single-Index Models

• Activity Number: 240
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Yao Yu*+ and Sally W. Thurston and Russ Hauser Hauser and Hua Liang
• Companies: University of Rochester and University of Rochester and Harvard School of Public Health and University of Rochester
• Keywords: Partially linear single-index models ; Focused information criterion ; Frequentist model averaging ; Profile least-squares

Abstract

This research is concerned with model selection and model averaging procedures for partially linear single-index models (PLSIM). The profile least-squares procedure is employed to estimate regression coefficients for the full model and submodels. We show that the estimators obtained from the profile least-squares procedure are asymptotically normal. We also derive the focused information criterion (FIC) and develop the frequentist model average (FMA) estimators for PLSIM. In addition, we construct proper confidence intervals for FMA and FIC estimators, a special case of FMA estimators. Monte Carlo studies are performed to demonstrate the superiority of the proposed method over the full model, and over models chosen by AIC or BIC in terms of coverage probability and mean squared error. Our approach is further applied to real data from a male fertility study to explore potential factors related to sperm concentration and estimate the relationship between sperm concentration and monobutyl phthalate.