Profile Thresholded Partial Correlation Approach for Variable Selection in Partial Linear Models

• Activity Number: 143
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Lejia Lou*+ and Runze Li
• Companies: and The Pennsylvania State University
• Keywords: Variable Selection ; Profile technique ; thresholded partial correlation approach ; partial linear models ; penalized profile approach ; partial faithfulness

Abstract

Partial linear models are becoming increasingly popular in nonparametric regression. They are good alternatives that retain advantages of both parametric and nonparametric models. In reality, it is crucial to identity the significant predictors in partial linear models. Stepwise deletion and best-subset can be extended to do variable selection in partial linear models, but they pose great challenges on implementation. To avoid repeating estimating the nonparametric part of each submodel, FanLi(2004) proposed the penalized profile approach, which utilizes the profile technique. This approach reduces the computation cost dramatically. With the concept of partial faithfulness, we extend the thresholded partial correlation approach to partial linear models based on the profile technique, and we call this extension the profile thresholded partial correlation approach. Under some regularity condition, we show that the resulting estimate of the coefficients are consistent,and nonparametric functions are asymptotically normally distributed. Simulation studies suggest that the profile thresholded partial correlation approach performs as well as the penalized profile approach with the SCAD