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August 2010 Varying-coefficient functional linear regression
Yichao Wu, Jianqing Fan, Hans-Georg Müller
Bernoulli 16(3): 730-758 (August 2010). DOI: 10.3150/09-BEJ231

Abstract

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression models is a regression parameter function in one or two arguments. 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 modeled 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 its 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. A practical version is developed and is shown to perform better than functional linear regression for longitudinal data. We investigate the asymptotic properties of varying-coefficient functional linear regression and establish consistency properties.

Citation

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Yichao Wu. Jianqing Fan. Hans-Georg Müller. "Varying-coefficient functional linear regression." Bernoulli 16 (3) 730 - 758, August 2010. https://doi.org/10.3150/09-BEJ231

Information

Published: August 2010
First available in Project Euclid: 6 August 2010

zbMATH: 1220.62046
MathSciNet: MR2730646
Digital Object Identifier: 10.3150/09-BEJ231

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

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Vol.16 • No. 3 • August 2010
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