Methodology and theory for partial least squares applied to functional data

By Aurore Delaigle, Peter Hall. 2012

153 citations recorded by the source corpus.

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.

Subfields: Analytical Chemistry, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1f8ef19e0897633659ce6cd4ac176c07ccf51c6b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Peter Hall, functional data analysis and random objects (2016, methodology): “In the 2012 paper (Delaigle and Hall, 2012b), a functional version of Fisher’s linear discriminant analysis was considered.”
Partial least squares prediction in high-dimensional regression (2019, background): “Delaigle and Hall [16] extended it to functional data.”
Variable selection in functional data classification: a maxima-hunting proposal (2013, methodology): “he use of the classical Fisher’s discriminant rule LDA (after dimension reduction) provides worse results than the nonparametric k-NN rule. An example of superiority of a linear classier is shown in Delaigle and Hall (2012b) where an asymptotic optimality result is provided. In addition, under some ”
Functional Principal Component Regression and Functional Partial Least‐squares Regression: An Overview and a Comparative Study (2017, methodology): “Regarding the asymptotic behavior of the estimator β̂PLS in (20), Preda and Saporta (2005) stated the consistency of β̂PLS to estimate β, although, as noted by Delaigle and Hall (2012), without a proof and without regularity conditions or convergence rates. Delaigle and Hall (2012) presented”
Selection of time instants and intervals with Support Vector Regression for multivariate functional data (2020, methodology): “Some dimensionality reduction techniques for linear regression in FDA have been introduced, such as principal component regression or partial least squares, Aguilera et al. (1997), Delaigle and Hall (2012), Preda and Saporta (2005,) and Reiss and Ogden (2007).”
On the Use of Reproducing Kernel Hilbert Spaces in Functional Classification (2015, methodology): “Our purpose here is to show that the setup of Theorem 3 (that is, Theorem 1 in Delaigle and Hall (2012)) can be analysed from the point of view of RKHS theory.”
Estimation in functional linear quantile regression (2012, methodology): “A potential drawback of using such basis functions is that, as discussed in [15], using the “first” m basis functions is less motivated.”