A simple numerical method of estimating the contribution of reference value uncertainties to sample-specific uncertainties in multivariate regression

The development of a sample-specific standard error of prediction (SS-SEP) for multivariate methods has been a major topic in the chemometrics literature. The expressions are, however, dependent on the predictive algorithm used. This study proposes a general and relatively economical numerical approach to the problem independent of the prediction algorithm used that potentially provides a validation technique for less established and more complex theoretical expressions. A comparison is then made to the standard errors estimated using the EIV approach in a PLS example. An important part of any such prediction interval is the contribution from uncertainties in reference values. The numerical method provided slightly optimistic standard errors, but these were sufficient to check the adequacy of the reference values and, for modest reference value uncertainties, for routine uncertainty estimation.