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April 2019 Partial least squares prediction in high-dimensional regression
R. Dennis Cook, Liliana Forzani
Ann. Statist. 47(2): 884-908 (April 2019). DOI: 10.1214/18-AOS1681

Abstract

We study the asymptotic behavior of predictions from partial least squares (PLS) regression as the sample size and number of predictors diverge in various alignments. We show that there is a range of regression scenarios where PLS predictions have the usual root-$n$ convergence rate, even when the sample size is substantially smaller than the number of predictors, and an even wider range where the rate is slower but may still produce practically useful results. We show also that PLS predictions achieve their best asymptotic behavior in abundant regressions where many predictors contribute information about the response. Their asymptotic behavior tends to be undesirable in sparse regressions where few predictors contribute information about the response.

Citation

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R. Dennis Cook. Liliana Forzani. "Partial least squares prediction in high-dimensional regression." Ann. Statist. 47 (2) 884 - 908, April 2019. https://doi.org/10.1214/18-AOS1681

Information

Received: 1 January 2017; Revised: 1 December 2017; Published: April 2019
First available in Project Euclid: 11 January 2019

zbMATH: 07033155
MathSciNet: MR3909954
Digital Object Identifier: 10.1214/18-AOS1681

Subjects:
Primary: 62J05
Secondary: 62F12

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 2 • April 2019
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