Partial least squares prediction in high-dimensional regression
type: Item
instance of: scholarly article
title: Partial least squares prediction in high-dimensional regression
zbMATH Open document ID: 1416.62389
DOI: 10.1214/18-AOS1681
author: R. Dennis Cook
author: Liliana Forzani
published in: The Annals of Statistics
publication date: 2019-03-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aos/1547197242
review text: The linear regression model \[ y=\mu+\beta^\top(X-\mathbb{E}(X))+\varepsilon \] is considered, where $y$ is univariate response, $X\in \mathbb{R}^p$ is random predictor vector, $\mu$ and $\beta$ are unknown coefficients, and the centered error $\varepsilon$ is independent of $X$. It is assumed that $(y, X)$ follows a nonsingular multivariate normal distribution and that the data $(y_i, X_i)$, $i=1,\dots, n,$ arise as independent copies of $(y, X)$. The partial least squares (PLS) estimator $\hat{\beta}$ developed in [\textit{R. D. Cook} et al., J. R. Stat. Soc., Ser. B, Stat. Methodol. 75, No. 5, 851--877 (2013; Zbl 1411.62137)] is used. The asymptotic behavior of PLS prediction is studied as $n$ and $p$ diverge in various alignments. It is shown that there is a range of regression scenarios where PLS predictors have $\sqrt{n}$ convergence rate, even when $n$ is essentially smaller than $p,$ and an even wider range where the rate is slower but may still produce practically useful results. It is shown also that PLS predictions achieve their best asymptotic behavior in abundant regressions where many predictors contribute information about the response.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 7033155
zbMATH Keywords: abundant regressions
zbMATH Keywords: dimension reduction
zbMATH Keywords: sparse regression
zbMATH Keywords: prediction
reviewed by: A. Kukush
MaRDI profile type: Publication
cites work: Sparse Partial Least Squares Regression for Simultaneous Dimension Reduction and Variable Selection
cites work: Q4217298
cites work: Big data and partial least‐squares prediction
cites work: Prediction in abundant high-dimensional linear regression
cites work: Envelopes and Partial Least Squares Regression
cites work: Dimension reduction in regression without matrix inversion
cites work: Q3580580
cites work: Methodology and theory for partial least squares applied to functional data
cites work: Weighted envelope estimation to handle variability in model selection
cites work: An Interpretation of Partial Least Squares
cites work: Q3198724
cites work: Q4203566
cites work: Q3996916
cites work: Q4272679
cites work: Partial Least Squares Estimator for Single-Index Models
cites work: On partial least squares dimension reduction for microarray-based classification: a simulation study
cites work: Q3965546
Wikidata QID: Q128606336
Recommended article: Shrinkage structure of partial least squares
Recommended article: Q4323473
Recommended article: An Interpretation of Partial Least Squares
Recommended article: Big data and partial least‐squares prediction
Recommended article: On the structure of partial least squares regression
Recommended article: Partial Least Squares: A First‐order Analysis
Recommended article: Partial least squares algorithm yields shrinkage estimators
description: scientific article; zbMATH DE number 7033155