Open Access
February 2012 Methodology and theory for partial least squares applied to functional data
Aurore Delaigle, Peter Hall
Ann. Statist. 40(1): 322-352 (February 2012). DOI: 10.1214/11-AOS958


The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares estimator of slope is either used to construct linear predictive models, or as a tool to project the data onto a one-dimensional quantity that is employed for further statistical analysis. Although the partial least squares approach is often viewed as an attractive alternative to projections onto the principal component basis, its properties are less well known than those of the latter, mainly because of its iterative nature. We develop an explicit formulation of partial least squares for functional data, which leads to insightful results and motivates new theory, demonstrating consistency and establishing convergence rates.


Download Citation

Aurore Delaigle. Peter Hall. "Methodology and theory for partial least squares applied to functional data." Ann. Statist. 40 (1) 322 - 352, February 2012.


Published: February 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1246.62084
MathSciNet: MR3014309
Digital Object Identifier: 10.1214/11-AOS958

Primary: 62G08

Keywords: central limit theorem , computational algorithm , consistency , Convergence rates , functional linear models , generalized Fourier basis , principal components , projection , stochastic expansion

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • February 2012
Back to Top