Multivariate Calibration — Direct and Indirect Regression Methodology

This paper tries first to introduce and motivate the methodology of multivariate calibration. Next a review is given, mostly avoiding technicalities, of the somewhat messy theory of the subject. Two approaches are distinguished: the estimation approach (controlled calibration) and the prediction approach (natural calibration). Among problems discussed are the choice of estimator, the choice of confidence region, methodology for handling situations with more variables than observations, near-collinearities (with counter-measures like ridge type regression, principal components regression, partial least squares regression and continuum regression), pretreatment of data, and cross-validation vs true prediction. Examples discussed in detail concern estimation of the age of a rhinoceros from its horn lengths (low-dimensional), and nitrate prediction in waste-water from high-dimensional spectroscopic measurements.