Functional linear regression via canonical analysis

Abstract

We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of functional linear regression analysis. A specific procedure for the estimation of the regression parameter function using canonical expansions is proposed and compared with an established functional principal component regression approach. As an example of an application, we present an analysis of mortality data for cohorts of medflies, obtained in experimental studies of aging and longevity.

Published in at http://dx.doi.org/10.3150/09-BEJ228 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (4)

• Functional linear regression analysis for longitudinal data
• Generalized functional linear models
• Methodology and convergence rates for functional linear regression
• The delta method for analytic functions of random operators with application to functional data

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• Functional Linear Regression: Dependence and Error Contamination
• Nonlinear Mixed-effects Scalar-on-function Models and Variable Selection for Kinematic Upper Limb Movement Data
• Individual Heterogeneity Learning in Distributional Data Response Additive Models
• Asymmetric canonical correlation analysis of Riemannian and high-dimensional data