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Pure Appl. Chem., 2006, Vol. 78, No. 3, pp. 633-661


Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report)

Alejandro C. Olivieri1*, Nicolaas M. Faber2, Joan Ferré3, Ricard Boqué3, John H. Kalivas4 and Howard Mark5

1 Departamento de Química Analítica, Facultad de Ciencias Bioquímicas y Farmacéuticas, Universidad Nacional de Rosario, Suipacha 531, Rosario S2002LRK, Argentina
2 Chemometry Consultancy, Rubensstraat 7, 6717 VD Ede, The Netherlands
3 Department of Analytical and Organic Chemistry, Rovira i Virgili University, 43007 Tarragona, Spain
4 Department of Chemistry, Idaho State University, Pocatello, ID 83209, USA
5 Mark Electronics, 69 Jamie Court, Suffern, NY 10901, USA

Abstract: This paper gives an introduction to multivariate calibration from a chemometrics perspective and reviews the various proposals to generalize the well-established univariate methodology to the multivariate domain. Univariate calibration leads to relatively simple models with a sound statistical underpinning. The associated uncertainty estimation and figures of merit are thoroughly covered in several official documents. However, univariate model predictions for unknown samples are only reliable if the signal is sufficiently selective for the analyte of interest. By contrast, multivariate calibration methods may produce valid predictions also from highly unselective data. A case in point is quantification from near-infrared (NIR) spectra. With the ever-increasing sophistication of analytical instruments inevitably comes a suite of multivariate calibration methods, each with its own underlying assumptions and statistical properties. As a result, uncertainty estimation and figures of merit for multivariate calibration methods has become a subject of active research, especially in the field of chemometrics.