Varying-Coefficient Functional Linear Regression

• Activity Number: 661
• Type: Topic Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yichao Wu*+ and Jianqing Fan and Hans-Georg Mueller
• Companies: North Carolina State University and Princeton University and University of California, Davis
• Keywords: Asymptotic ; eigenfunctions ; functional data analysis ; local polynomial smoothing ; longitudinal data ; varying coefficient models

Abstract

Functional linear regression analysis aims to model regression relations which include a functional predictor. If in addition one has scalar predictors, as is often the case in applications to longitudinal studies, the question arises how to incorporate these into a functional regression model. We study a varying-coefficient approach where the scalar covariates are modelled as additional arguments of the regression parameter function. This extension of the functional linear regression model is analogous to the extension of conventional linear regression models to varying coefficient models, and shares the advantages such as increased flexibility, however the details of this extension are more challenging in the functional case. Our methodology combines smoothing methods with regularization by truncation at a finite number of functional principal components.