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Multivariate Calibration — Direct and Indirect Regression Methodology

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  • Rolf Sundberg

Abstract

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.

Suggested Citation

  • Rolf Sundberg, 1999. "Multivariate Calibration — Direct and Indirect Regression Methodology," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 161-207, June.
  • Handle: RePEc:bla:scjsta:v:26:y:1999:i:2:p:161-207
    DOI: 10.1111/1467-9469.00144
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    Cited by:

    1. Jensen, D.R. & Ramirez, D.E., 2009. "Concentration reversals in ridge regression," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2237-2241, November.
    2. Lin, Chun-Sui & Huang, Mong-Na Lo, 2010. "Optimal designs for estimating the control values in multi-univariate regression models," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1055-1066, May.
    3. Paolo Vidoni, 2003. "Prediction and calibration in generalized linear models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 169-185, March.
    4. P. J. Brown & M. Vannucci & T. Fearn, 2002. "Bayes model averaging with selection of regressors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 519-536, August.
    5. Lynn R. LaMotte & Jeffrey D. Wells, 2016. "Inverse prediction for multivariate mixed models with standard software," Statistical Papers, Springer, vol. 57(4), pages 929-938, December.
    6. Francesca DE BATTISTI & Silvia SALINI & Alberto CRESCENTINI, 2004. "Statistical calibration of psychometric tests," Departmental Working Papers 2004-16, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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