Generalized error-dependent prediction uncertainty in multivariate calibration

Most of the current expressions used to calculate figures of merit in multivariate calibration have been derived assuming independent and identically distributed (iid) measurement errors. However, it is well known that this condition is not always valid for real data sets, where the existence of many external factors can lead to correlated and/or heteroscedastic noise structures. In this report, the influence of the deviations from the classical iid paradigm is analyzed in the context of error propagation theory. New expressions have been derived to calculate sample dependent prediction standard errors under different scenarios. These expressions allow for a quantitative study of the influence of the different sources of instrumental error affecting the system under analysis. Significant differences are observed when the prediction error is estimated in each of the studied scenarios using the most popular first-order multivariate algorithms, under both simulated and experimental conditions.