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. Partial least square (PLS) regression is a multivariate technique developed to solve multicollinearity and high dimensionality in covariates. We propose a new estimator for the covariance matrix of the estimator of PLS coefficients and prove its unbiasedness and consistency. We conduct simulations to compare the proposed estimator with a modified jackknife estimator, showing the accuracy and computational efficiency of the new estimator. We illustrate the proposed results with three chemical data sets, which show its potential in chemometrical problems.