Open Access
February 2020 Envelope-based sparse partial least squares
Guangyu Zhu, Zhihua Su
Ann. Statist. 48(1): 161-182 (February 2020). DOI: 10.1214/18-AOS1796


Sparse partial least squares (SPLS) is widely used in applied sciences as a method that performs dimension reduction and variable selection simultaneously in linear regression. Several implementations of SPLS have been derived, among which the SPLS proposed in Chun and Keleş (J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25) is very popular and highly cited. However, for all of these implementations, the theoretical properties of SPLS are largely unknown. In this paper, we propose a new version of SPLS, called the envelope-based SPLS, using a connection between envelope models and partial least squares (PLS). We establish the consistency, oracle property and asymptotic normality of the envelope-based SPLS estimator. The large-sample scenario and high-dimensional scenario are both considered. We also develop the envelope-based SPLS estimators under the context of generalized linear models, and discuss its theoretical properties including consistency, oracle property and asymptotic distribution. Numerical experiments and examples show that the envelope-based SPLS estimator has better variable selection and prediction performance over the SPLS estimator (J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 3–25).


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Guangyu Zhu. Zhihua Su. "Envelope-based sparse partial least squares." Ann. Statist. 48 (1) 161 - 182, February 2020.


Received: 1 April 2017; Revised: 1 September 2018; Published: February 2020
First available in Project Euclid: 17 February 2020

zbMATH: 07196534
MathSciNet: MR4065157
Digital Object Identifier: 10.1214/18-AOS1796

Primary: 62B05 , 62F12
Secondary: 62J05 , 62J12

Keywords: envelope model , Grassmann manifold , Partial least squares , sufficient dimension reduction

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 1 • February 2020
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