The Annals of Statistics

Methodology and theory for partial least squares applied to functional data

Aurore Delaigle and Peter Hall

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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

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

First available in Project Euclid: 4 April 2012

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Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression

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


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.

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