Estimation of partial least squares regression prediction uncertainty when the reference values carry a sizeable measurement error

The prediction uncertainty is studied when using a multivariate partial least squares regression (PLSR) model constructed with reference values that contain a sizeable measurement error. Several approximate expressions for calculating a sample-specific standard error of prediction have been proposed in the literature. In addition, Monte Carlo simulation methods such as the bootstrap and the noise addition method can give an estimate of this uncertainty. In this paper, two approximate expressions are compared with the simulation methods for three near-infrared data sets.