A non‐asymptotic analysis of the single component PLS regression

Luca Castelli, Irène Gannaz and Clément Marteau

Scandinavian Journal of Statistics, 2025, vol. 52, issue 4, 2314-2351

Abstract: This paper investigates some theoretical properties of the Partial Least Squares method. We focus our attention on the single‐component case, which provides a useful framework to understand the underlying mechanism. We provide a non‐asymptotic upper bound on the quadratic loss in prediction with high probability in a high‐dimensional regression context. The bound is attained thanks to a preliminary regularization on the first PLS component. In a second time, we extend these results to the sparse Partial Least Squares approach. In particular, we exhibit upper bounds similar to those obtained with the lasso algorithm, up to an additional restricted eigenvalue constraint on the design matrix.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/sjos.70028

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:52:y:2025:i:4:p:2314-2351

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0303-6898

Access Statistics for this article

Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist

More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association
Bibliographic data for series maintained by Wiley Content Delivery ().