Functional Linear Model with Zero-Value Coefficient Function at Sub-Region

• Activity Number: 523
• Type: Contributed
• Date/Time: Wednesday, August 5, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jianhui Zhou*+ and Naisyin Wang
• Companies: University of Virginia and Texas A&M University
• Keywords: Functional linear regression ; Group smoothly clipped absolute deviation approach ; Null region

Abstract

We propose a shrinkage method to estimate the coefficient function in a functional linear regression model when the value of the coefficient function is zero at certain sub-region. The primary goal is to perform inferences for the nonparametric estimate of the coefficient function and to identify the null region in which the function is zero. Our proposal consists of two stages. In stage one, Dantzig selector is employed to provide initial location of the null region. In stage two, we propose to use a group SCAD approach to refine the estimated location of the null region and to provide the estimate and inference procedures for the coefficient function. Theoretically, we show that our estimator enjoys the desired Oracle property. The performance of the proposed method is illustrated through a simulation study.