Multivariate Calibration
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1982 · Volume 44 · Issue 3
DOI: 10.1111/j.2517-6161.1982.tb01209.x
Abstract
A set ofqresponses Y = (Y1,…, Yq)Tare determined by a set ofpexplanatory variables x = (X1,…,Xp)T. A set oflobserved vectors Y are available at a single unknown x and it is desired to draw inferences about this unknown vector X. In order to do this calibrating data is available jointly on (Y, X) where two situations are distinguished (i), x is controlled, (ii) x is random. Using orthodox sampling theory on the one hand and Bayesian methods on the other hand point estimators and confidence regions are derived and contrasted. A procedure for selection of a subset of responses is given. Finally a comparison is made of the methods on data from (a) a random calibration experiment of wheat quality using an infrared spectrometer and (b) a controlled experiment of point finish.
Keywords
calibration, multivariate regression, prediction, controlled and random experimentation, bayes
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