Bernoulli

  • Bernoulli
  • Volume 16, Number 3 (2010), 705-729.

Functional linear regression via canonical analysis

Guozhong He, Hans-Georg Müller, Jane-Ling Wang, and Wenjing Yang

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 16, Number 3 (2010), 705-729.

Dates
First available in Project Euclid: 6 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1281099881

Digital Object Identifier
doi:10.3150/09-BEJ228

Mathematical Reviews number (MathSciNet)
MR2730645

Zentralblatt MATH identifier
1220.62076

Keywords
canonical components covariance operator functional data analysis functional linear model longitudinal data parameter function stochastic process

Citation

He, Guozhong; Müller, Hans-Georg; Wang, Jane-Ling; Yang, Wenjing. Functional linear regression via canonical analysis. Bernoulli 16 (2010), no. 3, 705--729. doi:10.3150/09-BEJ228. https://projecteuclid.org/euclid.bj/1281099881


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