title: Generalized error-dependent prediction uncertainty in multivariate calibration.
abstract: 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.
authors.affiliation: Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Instituto de Química de Rosario (IQUIR-CONICET), Suipacha 531, Rosario S2002LRK, Argentina.
authors.forename: Franco
authors.initials: F
authors.lastname: Allegrini
authors.affiliation: Department of Chemistry, Dalhousie University, P.O. Box 15000, Halifax, Nova Scotia, B3H 4R2, Canada. Electronic address: peter.wentzell@dal.ca.
authors.forename: Peter D
authors.initials: PD
authors.lastname: Wentzell
authors.affiliation: Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Instituto de Química de Rosario (IQUIR-CONICET), Suipacha 531, Rosario S2002LRK, Argentina. Electronic address: olivieri@iquir-conicet.gov.ar.
authors.forename: Alejandro C
authors.initials: AC
authors.lastname: Olivieri
keywords: Correlated errors; Error propagation; Heteroscedastic errors; Measurement noise; Multivariate calibration; Prediction errors