Single-Index Model with Diverging Number of Index Parameters

• Activity Number: 477
• Type: Topic Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Guannan Wang*+ and Lily Wang
• Companies: University of Georgia and The University of Georgia
• Keywords: Single-index Prediction Model ; Variable Selection ; Oracle Property ; Nonparametric Regression ; B-spline ; SCAD

Abstract

Single-index models are useful and fundamental tools for handling ``curse of dimensionality'' problems in nonparametric regression. Along with that, variable selection also plays an important role in such model building process when the index vectors are high-dimensional. Many procedures have been developed for estimation and variable selection for single-index models when the number of index parameters are fixed. In this work, we consider single-index prediction models, which are robust against model mis-specifications, in sparse and high-dimensional settings. We apply the SCAD penalty and spline basis function expansion to perform estimation and variable selection in the framework of a diverging number of index parameters. Under regularity conditions, the proposed variable selection method is shown to have the oracle property when the number of parameters tends to infinity as the sample size increases. A fast and efficient variable selection algorithm is developed to estimate parameters and select significant variables simultaneously. The finite sample behavior of the proposed method is evaluated with simulation studies and illustrated by a real data example.