# Linear comparative calibration with correlated measurements

Gejza Wimmer; Viktor Witkovský

Kybernetika (2007)

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

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topWimmer, 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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- 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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