Domain Selection for Varying Coefficient Model via Local Polynomial Regression

• Activity Number: 29
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Dehan Kong*+ and Howard Bondell and Yichao Wu
• Companies: North Carolina State University and North Carolina State University and North Carolina State University
• Keywords: Domain selection ; Local polynomial regression ; SCAD ; Varying coefficient model

Abstract

In this article, we consider the varying coefficient model which allows for the relationship between the predictors and response to vary across the region of interest, such as time. In applications, it is common that certain predictors only affect the response in particular regions and not everywhere. This corresponds to identifying regions where the varying coefficient is zero. To solve this problem, we will incorporate local polynomial smoothing and penalized regression into one framework. Efficient algorithms of choosing the appropriate bandwidth as well as solving the penalized regression problem are discussed. We establish asymptotic properties of our penalized estimators and show that they enjoy the oracle properties in the sense that they have the same bias and asymptotic variance as the local polynomial estimators. The method proposed is examined by simulations and on a real data example.