Multi-way figures of merit in the presence of heteroscedastic and correlated instrumental noise: Unfolded partial least-squares with residual multi-linearization

In the presence of correlated and/or heteroscedastic noise, i.e., for measurement noise which is not independent and identically distributed (iid), new expressions are required to estimate multi-way calibration figures of merit. They are derived in the present report, with focus towards a useful multi-way approach based on unfolded partial least-squares with residual multi-linearization. The expressions allow one to estimate figures of merit under a generalized noise propagation scenario, and to gain insight into the various uncertainty sources contributing to the overall prediction error and limit of detection. Through the study of both simulated and experimental data, it is shown that significant differences exist between the values estimated assuming an iid noise structure and when the underlying structure deviates from this classical paradigm.