JSM 2011 Online Program

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Abstract Details

Activity Number: 127
Type: Contributed
Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #301457
Title: Semiparametric Functional Linear Model
Author(s): Dehan Kong*+ and Fang Yao and Hao "Helen" Zhang
Companies: North Carolina State University and University of Toronto and North Carolina State University
Address: 3002G Kings Ct, Raleigh, NC, 27606,
Keywords: Functional data analysis ; Functional linear model ; Model selection ; Principal components ; SCAD ; Semiparametric
Abstract:

We propose and study a new class of semiparametric functional regression models. With a scalar response, multiple covariates are collected, a large number of which are time-independent and a few may be functional with underlying processes. The goal is to jointly model the functional and non-functional predictors, identifying important scalar covariates while taking into account the functional covariate. In particular we exploit a unified linear structure to incorporate the functional predictor as in classical functional linear models that is of nonparametric feature. Simultaneously we include a potentially large number of scalar predictors as the parametric part that may be reduced to a sparse representation. We propose an iterative procedure to perform variable selection and estimation, by naturally combining the functional principal component analysis (FPCA) and the smoothly clipped absolute deviation (SCAD) penalized regression under one framework. Theoretical and empirical investigation reveals that the efficient estimation regarding important scalar predictors can be obtained and enjoys the oracle property, despite contamination of the noise-prone functional covariate.


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