Methodology and theory for partial least squares applied to functional data

TL;DR

This paper develops an explicit formulation of partial least squares for functional data, providing new theoretical insights, demonstrating consistency, and establishing convergence rates for its use in statistical modeling.

Contribution

It introduces a novel explicit formulation of PLS for functional data, enabling rigorous theoretical analysis and understanding of its properties.

Findings

Demonstrates consistency of the PLS estimator for functional data.

Establishes convergence rates for the PLS procedure.

Provides insights into the iterative nature of PLS in functional data analysis.

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.