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Abstract Details

Activity Number: 375
Type: Invited
Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
Sponsor: ENAR
Abstract - #303561
Title: Semiparametric Functional Linear Model with High-Dimensional Covariates
Author(s): Fang Yao*+ and Hao Helen Zhang and Dehan Kong
Companies: University of Toronto and North Carolina State University and North Carolina State University
Address: Department of Statistics, Toronto, ON, , Canada
Keywords: Functional data analysis ; Functional linear model ; Model selection ; Principal components ; SCAD ; Semiparametrics

We propose and study a new class of semiparametric functional regression models motivated by the complex nature of data encountered in modern scientific experiments. With a scalar response, multiple covariates are collected, a large number of which are time-independent and directly observed 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. 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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