JSM 2004 - Toronto

Abstract #301269

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Activity Number: 188
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #301269
Title: A Smoothing-spline Approach to Linear Regression for Functional Data
Author(s): Yehua Li*+
Companies: Texas A&M University
Address: Dept. of Statistics, College Station, TX, 77840,
Keywords: functional linear model ; reproducing kernel Hilbert space ; smoothing spline
Abstract:

Consider the linear regression model where the dependent variable is a scalar and the independent variable is a function observed on a finite interval. Ramsay and Silverman (1997) proposed a functional linear model, in which the mean of the response equals to an intercept plus the integral of the independent variable with a weight function \beta(t). To estimate the weight function, a finite dimension subspace approximation using a given set of basis functions was proposed. As an alternative, we show this model could be adopted in a Reproducing Kernel Hilbert Space framework and a smoothing-spline estimator for the weight function is developed. Methods of selecting the smoothing parameter are discussed. Some asymptotic property is explored and serum lipoprotein data are used to illustrate the approach. Also, some simulations are conducted to make a comparison with the basis function approach.

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