@article{387406e0e5774d0caf6d741a34216cd4,
title = "A new estimator for the covariance of the PLS coefficients estimator with applications to chemical data",
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.",
keywords = "Monte Carlo method, PLS regression, R software, covariance matrix, jackknife method, standard error",
author = "Mart{\'i}nez, {Jos{\'e} L.} and V{\'i}ctor Leiva and Helton Saulo and Fabrizio Ruggeri and Arteaga, {Gean C.}",
note = "Funding Information: The authors thank the Editors and Referees for their constructive comments on an earlier version of this manuscript which resulted in this improved version. J.L. Mart?nez would like to thank M.H. Spirit and I.J. Galilean for helpful discussions and comments on this work and the Computational Laboratory of the Universidad del Sin?. Research work of V. Leiva was partially supported by FONDECYT 1160868 grant from the Chilean government. Funding Information: The authors thank the Editors and Referees for their constructive comments on an earlier version of this manuscript which resulted in this improved version. J.L. Mart{\'i}nez would like to thank M.H. Spirit and I.J. Galilean for helpful discussions and comments on this work and the Computational Laboratory of the Universidad del Sin{\'u}. Research work of V. Leiva was partially supported by FONDECYT 1160868 grant from the Chilean government. Publisher Copyright: {\textcopyright} 2018 John Wiley & Sons, Ltd.",
year = "2018",
month = dec,
doi = "10.1002/cem.3069",
language = "English",
volume = "32",
journal = "Journal of Chemometrics",
issn = "0886-9383",
number = "12",
}