Automatic Structure Selection in Semiparametric Models

• Activity Number: 375
• Type: Invited
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Hao Helen Zhang*+ and Guang Cheng and Yufeng Liu
• Companies: University of Arizona and Purdue University and The University of North Carolina at Chapel Hill
• Keywords: partial linear models ; RKHS ; smoothing spline ANOVA ; selection consistency ; sparsity ; model selection

Abstract

Partial linear models provide good compromises between linear models and nonparametric models. How to determine which covariates have linear effects and which have nonlinear effects is a fundamental and theoretically challenging problem in multiple regression. Most existing methods in practice are largely ad hoc and lack theoretical justifications. In this work, we tackle the structure selection problem from a new perspective in model selection. A unified regularization framework in reproducing kernel Hilbert space (RKHS) is developed to automatically distinguish linearity and nonlinearity of the covariates, and at the same time estimate their effects. We show that the new estimator can discover the underlying true model structure correctly as the sample size goes to infinity. Numerical examples are presented to illustrate performance of the new procedure under various regression settings.