Premium
A new estimator for the covariance of the PLS coefficients estimator with applications to chemical data
Author(s) -
Martínez José L.,
Leiva Víctor,
Saulo Helton,
Ruggeri Fabrizio,
Arteaga Gean C.
Publication year - 2018
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.3069
Subject(s) - multicollinearity , univariate , estimator , mathematics , covariance , jackknife resampling , statistics , covariance matrix , estimation of covariance matrices , consistency (knowledge bases) , multivariate statistics , partial least squares regression , curse of dimensionality , minimum variance unbiased estimator , monte carlo method , econometrics , linear regression , geometry
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.