A new estimator for the covariance of the PLS coefficients estimator with applications to chemical data

José L. Martínez, Víctor Leiva, Helton Saulo, Fabrizio Ruggeri, Gean C. Arteaga

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Partial least squares (PLS) regression is a multivariate technique developed to solve the problem of multicollinearity and high dimensionality in explanatory variables. Several efforts have been made to improve the estimation of the covariance matrix of the PLS coefficients estimator. We propose a new estimator for this covariance matrix and prove its unbiasedness and consistency. We conduct a Monte Carlo simulation study to compare the proposed estimator and one based on the modified jackknife method, showing the advantages of the new estimator in terms of accuracy and computational efficiency. We illustrate the proposed method with three univariate and multivariate real-world chemical data sets. In these illustrations, important findings are discovered because the conclusions of the studies change drastically when using the proposed estimation method in relation to the standard method, implying a change in the decisions to be made by the chemical practitioners.

Original languageEnglish
Article numbere3069
JournalJournal of Chemometrics
Volume32
Issue number12
DOIs
StatePublished - Dec 2018
Externally publishedYes

Keywords

  • Monte Carlo method
  • PLS regression
  • R software
  • covariance matrix
  • jackknife method
  • standard error

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