PLS: a new statistical insight through the prism of orthogonal polynomials
type: Dataset
description: Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting the response $Y$. In this paper we provide a new and explicit formula for the residuals. We show that the residuals are completely determined by the spectrum of the design matrix and by the noise on the observations. Because few are known on the behaviour of the PLS components we also investigate their statistical properties in a regression context. New results on regression and prediction error for PLS are stated under the assumption of a low variance of the noise.
issued: 2026-05-05T10:29:30.937126
language: en
modified: 2026-05-05T10:29:30.937130
contact point: Organization
  fn: CCSD
keyword: constrainsted-least-square
keyword: dimension-reduction
keyword: infoeu-reposemanticspreprint
keyword: mathmath-stmathematics-mathstatistics-mathst
keyword: multicollinearity
keyword: multivariate-regression
keyword: orthogonal-polynomials
keyword: partial-least-square
keyword: prediction-error
keyword: preprints-working-papers-
keyword: statthstatistics-statstatistics-theory-statth
landing page: https://hal.science/hal-00995049

PLS: a new statistical insight through the prism of orthogonal polynomials
type: Distribution
format: HTML
issued: 2026-05-05T10:29:30.938523
modified: 2026-05-05T10:29:30.923754
access URL: https://hal.science/hal-00995049

test_moissonnage_selune
type: Agent