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

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

Journal of Chemometrics 32 (2018) e3069

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.