Confidence Region for Calibration Function Coefficients

Petra Ráboňová 1  and Gejza Wimmer 2 , 3
  • 1 Faculty of Science, Masaryk University, 611 37, Brno
  • 2 Faculty of Science, Matej Bel University, 974 01, Banská Bystrica
  • 3 Mathematical Institute, Slovak Academy of Sciences, , 814 73, Bratislava


The paper deals with the comparative calibration model, i.e. with a situation when both variables are subject to errors. The calibration function is supposed to be a polynomial. From the statistical point of view, the model after linearization could be represented by the linear errors-in-variables (EIV) model. There are two different ways of using the Kenward and Roger’s type approximation to obtain the confidence region for calibration function coefficients. These two confidence regions are compared on a small simulation study. Calibration process and process of measuring with calibrated device are described under the assumption that the measuring errors are normally distributed.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Joint Committee for Guides in Metrology (JCGM). (2012). International vocabulary of metrology — Basic and general concepts and associated terms (VIM). 3rd edition, 2008 version with minor corrections. JCGM 200:2012.

  • [2] Kubáček, L. (2012). Foundations of Estimation Theory. Elsevier.

  • [3] Fišerová, E., Kubáček, L., Kunderová, P. (2007) Linear Statistical Models: Regularity and Singularities. Prague, Czech Republic: Academia.

  • [4] Kubáček, L., Kubáčková, L. (2000) Statistics and Metrology. (In Czech). Olomouc, Czech Republic: Palacký University Olomouc. (in Czech)

  • [5] Wimmer, G., Palenčár, R., Witkovský, V., Ďuriš, S. (2015). Vyhodnotenie kalibrácie meradiel: Štatistické metódy pre analýzu neistôt v metrológii (Evaluation of the Calibration of the Measuring Instruments: Statistical Methods for the Analysis of Uncertainties in Metrology). Bratislava, Slovak Republic: Slovak University of Technology in Bratislava (STU). (in Slovak)

  • [6] Rao, C.R., Kleffe, J. (1988) Estimation of Variance Components and Applications. North Holland.

  • [7] Kenward, M.G., Roger, J.H. (1997) Small sample inference for fixed effects from restricted maximum likelihood Biometrics, 53, 983–997.


Journal + Issues