JSM 2005 - Toronto

Abstract #303674

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 69
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #303674
Title: Penalized Spline Models for Functional Data
Author(s): Fang Yao*+ and Thomas Lee
Companies: Colorado State University and Colorado State University
Address: Department of Statistics, Fort Collins, CO, 80523, United States
Keywords: Asymptotics ; Functional data ; Penalized spline ; Principal components ; Smoothing ; Correlation
Abstract:

We propose an iterative estimation procedure for performing functional principal component analysis. The procedure aims at functional or longitudinal data where the repeated measurements from the same subject are correlated. An increasingly popular smoothing approach, penalized spline regression, is used to represent the group mean trends. This allows straightforward incorporation of covariates and simple implementation of inference procedures for coefficients. For the handling of the within-subject correlation, we develop an iterative procedure which would gradually reduce the dependence amongst the repeated measurements made for the same subject. The resulting data after iteration are theoretically shown to be asymptotically independent, which suggests that the general theory of penalized spline regression developed for independent data can also be applied to functional data. The effectiveness of the proposed procedure is demonstrated via a simulation study and applications to real data examples.

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