The Annals of Statistics

Methodology and theory for partial least squares applied to functional data

Aurore Delaigle and Peter Hall

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 40, Number 1 (2012), 322-352.

Dates
First available in Project Euclid: 4 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.aos/1333567192

Digital Object Identifier
doi:10.1214/11-AOS958

Mathematical Reviews number (MathSciNet)
MR3014309

Zentralblatt MATH identifier
1246.62084

Subjects
Primary: 62G08: Nonparametric regression

Keywords
Central limit theorem computational algorithm consistency convergence rates functional linear models generalized Fourier basis principal components projection stochastic expansion

Citation

Delaigle, Aurore; Hall, Peter. Methodology and theory for partial least squares applied to functional data. Ann. Statist. 40 (2012), no. 1, 322--352. doi:10.1214/11-AOS958. https://projecteuclid.org/euclid.aos/1333567192


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