Prediction intervals in Partial Least Squares regression via a new local linearization approach

Abstract

Univariate Partial Least Squares is a biased regression procedure for calibration and prediction widely used in chemometrics. To the best of our knowledge the distributional properties of the PLS regression estimator still remain unpublished and this leads to difficulties in performing inference-based procedures such as obtaining prediction intervals for new samples. Prediction intervals require the variance of the regression estimator to be known in order to evaluate the variance of the prediction. Because the nonlinearity of the regression estimator on the response variable, local linear approximation through the δ-method for the PLS regression vector have been proposed in the literature. In this paper we present a different local linearization which is carried out around the vector of the covariances between response and predictors, and covariances between predictors. This approach improves the previous ones in terms of bias and precision. Moreover, the proposed algorithm speeds up the calculations of the Jacobian matrix and performs better than recent efficient implementations.