Linear comparative calibration with correlated measurements

Gejza Wimmer; Viktor Witkovský

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 443-452
  • ISSN: 0023-5954

Abstract

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The paper deals with the linear comparative calibration problem, i. e. the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From statistical point of view the model could be represented by the linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimation the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the approximate confidence region for the parameters. The confidence limits are derived using the concept of Kenward and Roger [Kenward]. Their performance is investigated by simulation. The simulation results show that under reasonable restrictions the proposed confidence regions are very satisfactory for practical use.

How to cite

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Wimmer, Gejza, and Witkovský, Viktor. "Linear comparative calibration with correlated measurements." Kybernetika 43.4 (2007): 443-452. <http://eudml.org/doc/33869>.

@article{Wimmer2007,
abstract = {The paper deals with the linear comparative calibration problem, i. e. the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From statistical point of view the model could be represented by the linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimation the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the approximate confidence region for the parameters. The confidence limits are derived using the concept of Kenward and Roger [Kenward]. Their performance is investigated by simulation. The simulation results show that under reasonable restrictions the proposed confidence regions are very satisfactory for practical use.},
author = {Wimmer, Gejza, Witkovský, Viktor},
journal = {Kybernetika},
keywords = {linear calibration; analysis function; regression with errors- in-variables; Kenward–Roger type approximation; linear calibration; analysis function; regression with errors-in-variables; Kenward-Roger type approximation},
language = {eng},
number = {4},
pages = {443-452},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Linear comparative calibration with correlated measurements},
url = {http://eudml.org/doc/33869},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Wimmer, Gejza
AU - Witkovský, Viktor
TI - Linear comparative calibration with correlated measurements
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 443
EP - 452
AB - The paper deals with the linear comparative calibration problem, i. e. the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From statistical point of view the model could be represented by the linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimation the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the approximate confidence region for the parameters. The confidence limits are derived using the concept of Kenward and Roger [Kenward]. Their performance is investigated by simulation. The simulation results show that under reasonable restrictions the proposed confidence regions are very satisfactory for practical use.
LA - eng
KW - linear calibration; analysis function; regression with errors- in-variables; Kenward–Roger type approximation; linear calibration; analysis function; regression with errors-in-variables; Kenward-Roger type approximation
UR - http://eudml.org/doc/33869
ER -

References

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  1. Casella G., Berger R. L., Statistical Inference, Duxbury Advanced Series, Belmont 1990 Zbl0699.62001MR1051420
  2. Gleser L. J., Assessing uncertainty in measurement, Statistical Science 13 (1998), 277–290 (1998) Zbl1099.62502MR1665642
  3. Kenward M. G., Roger J. H., Small sample inference for fixed effects from restricted maximum likelihood, Biometrics 53 (1997), 983–997 (1997) Zbl0890.62042
  4. Kubáček L., Kubáčková L., One of the calibration Problems, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 36 (1997), 117–130 (1997) Zbl0959.62052MR1620541
  5. Kubáček L., Kubáčková L., Statistics and Metrology (in Czech), Univerzita Palackého v Olomouci, Olomouc 2000 
  6. Kubáčková L., Foundations of Experimental Data Analysis, CRC–Press, Boca Raton – Ann Arbor – London – Tokyo 1992 Zbl0875.62016MR1244322
  7. Rao C. R., Mitra K. S., Generalize Inverse of Matrices and Its Applications, Wiley, New York 1971 MR0338013
  8. Wimmer G., Witkovský, V., Savin A., Confidence region for parameters in replicated errors in variables model, In: COMPSTAT: Proc. in Computational Statistics – 16th Symposium, Prague (J. Antoch, ed.), Physica–Verlag, Heidelberg 2004, pp. 1987–1994 (1987) MR2173229

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