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Two models for linear comparative calibration

Published online by Cambridge University Press:  13 May 2013

G. Wimmer  and
V. Witkovský
G. Wimmer*
Affiliation:
Mathematical Institute, Slovak Academy of Sciences Bratislava, Slovak Republic Faculty of Natural Sciences, Matej Bel University Banská Bystrica, Slovak Republic Institute of Mathematics and Statistics, Masaryk University Brno, Czech Republic
V. Witkovský
Affiliation:
Institute of Measurement Science, Slovak Academy of Sciences Bratislava, Slovak Republic
*
⋆ Correspondence: [email protected]
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Abstract

We consider the comparative calibration problem in the case when linear relationship is assumed between two considered measuring devices with possibly different units and precisions. The first method for obtaining the approximate confidence region for unknown parameters of the calibration line applies the maximum likelihood estimators of the unknown parameters. The second method is based on estimation of the calibration line via replicated errors-in-variables model. Essential point in this approach is approximation of the small sample distribution of the Wald-type test statistic. This enables to construct the interval estimators for the multiple-use calibration case.

Keywords

Calibration problemmultiple-use calibrationmaximum likelihood estimatorerrors-in-variables modelKenward-Roger approximation
Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 3 , Issue 3 , 2012 , pp. 179 - 184
Copyright
© EDP Sciences 2013

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References

Kenward, M.G., Roger, J.H., Small sample inference for fixed effects from restricted maximum likelihood, Biometrics 53, 983–997 (1997) CrossRefGoogle ScholarPubMed
G. Wimmer, V. Witkovský, A. Savin, Confidence region for parameters in replicated errors in variables model, in Proceedings in Computational Statistics (COMPSTAT 2004), Prague, Czech Republic (Physica-Verlag, 2004), pp. 1987–1994
Wimmer, G., Witkovský, V., Scheffé-type confidence region for the calibration line, Austrian J. Stat. 35, 397–406 (2006) Google Scholar
Wimmer, G., Witkovský, V., Linear comparative calibration with correlated measurements, Kybernetika 43, 443–452 (2007) Google Scholar
Wimmer, G., Witkovský, V., Univariate linear calibration via replicated errors-in-variables model, J. Stat. Comp. Simul. 77, 213–227 (2007) CrossRefGoogle Scholar
Matušeková, R., Linear calibration, J. Electr. Eng. 57, 114–116 (2006) Google Scholar
H. Scheffé, The Analysis of Variance (Wiley, New York, 1959)
Satterthwaite, F.E., An approximate distribution of estimates of variance components, Biomet. Bull. 2, 110–114 (1946) CrossRefGoogle ScholarPubMed