Geodesic
Linear comparative calibration with correlated measurements
Kybernetika, Tome 43 (2007) no. 4, pp. 443-452 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 60F05, 62E10, 62F10, 62F25, 62H12, 62J05, 65C60
Keywords: linear calibration; analysis function; regression with errors- in-variables; Kenward–Roger type approximation 
@article{KYB_2007_43_4_a4,
     author = {Wimmer, Gejza and Witkovsk\'y, Viktor},
     title = {Linear comparative calibration with correlated measurements},
     journal = {Kybernetika},
     pages = {443--452},
     year = {2007},
     volume = {43},
     number = {4},
     mrnumber = {2377922},
     zbl = {1135.62059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007_43_4_a4/}
}
TY  - JOUR
AU  - Wimmer, Gejza
AU  - Witkovský, Viktor
TI  - Linear comparative calibration with correlated measurements
JO  - Kybernetika
PY  - 2007
SP  - 443
EP  - 452
VL  - 43
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/KYB_2007_43_4_a4/
LA  - en
ID  - KYB_2007_43_4_a4
ER  - 
%0 Journal Article
%A Wimmer, Gejza
%A Witkovský, Viktor
%T Linear comparative calibration with correlated measurements
%J Kybernetika
%D 2007
%P 443-452
%V 43
%N 4
%U http://geodesic.mathdoc.fr/item/KYB_2007_43_4_a4/
%G en
%F KYB_2007_43_4_a4
Wimmer, Gejza; Witkovský, Viktor. Linear comparative calibration with correlated measurements. Kybernetika, Tome 43 (2007) no. 4, pp. 443-452. http://geodesic.mathdoc.fr/item/KYB_2007_43_4_a4/

[3] Casella G., Berger R. L.: Statistical Inference. Duxbury Advanced Series, Belmont 1990 | MR | Zbl

[4] Gleser L. J.: Assessing uncertainty in measurement. Statistical Science 13 (1998), 277–290 | MR | Zbl

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

[6] Kubáček L., Kubáčková L.: One of the calibration Problems. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 36 (1997), 117–130 | MR | Zbl

[7] Kubáček L., Kubáčková L.: Statistics and Metrology (in Czech). Univerzita Palackého v Olomouci, Olomouc 2000

[8] Kubáčková L.: Foundations of Experimental Data Analysis. CRC–Press, Boca Raton – Ann Arbor – London – Tokyo 1992 | MR | Zbl

[9] Rao C. R., Mitra K. S.: Generalize Inverse of Matrices and Its Applications. Wiley, New York 1971 | MR

[10] 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 | MR