| Title:
|
Linear comparative calibration with correlated measurements (English) |
| Author:
|
Wimmer, Gejza |
| Author:
|
Witkovský, Viktor |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2007 |
| Pages:
|
443-452 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
linear calibration |
| Keyword:
|
analysis function |
| Keyword:
|
regression with errors- in-variables |
| Keyword:
|
Kenward–Roger type approximation |
| MSC:
|
60F05 |
| MSC:
|
62E10 |
| MSC:
|
62F10 |
| MSC:
|
62F25 |
| MSC:
|
62H12 |
| MSC:
|
62J05 |
| MSC:
|
65C60 |
| idZBL:
|
Zbl 1135.62059 |
| idMR:
|
MR2377922 |
| . |
| Date available:
|
2009-09-24T20:25:21Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135786 |
| . |
| Reference:
|
[3] Casella G., Berger R. L.: Statistical Inference.Duxbury Advanced Series, Belmont 1990 Zbl 0699.62001, MR 1051420 |
| Reference:
|
[4] Gleser L. J.: Assessing uncertainty in measurement.Statistical Science 13 (1998), 277–290 Zbl 1099.62502, MR 1665642 |
| Reference:
|
[5] Kenward M. G., Roger J. H.: Small sample inference for fixed effects from restricted maximum likelihood.Biometrics 53 (1997), 983–997 Zbl 0890.62042 |
| Reference:
|
[6] Kubáček L., Kubáčková L.: One of the calibration Problems.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 36 (1997), 117–130 Zbl 0959.62052, MR 1620541 |
| Reference:
|
[7] Kubáček L., Kubáčková L.: Statistics and Metrology (in Czech).Univerzita Palackého v Olomouci, Olomouc 2000 |
| Reference:
|
[8] Kubáčková L.: Foundations of Experimental Data Analysis.CRC–Press, Boca Raton – Ann Arbor – London – Tokyo 1992 Zbl 0875.62016, MR 1244322 |
| Reference:
|
[9] Rao C. R., Mitra K. S.: Generalize Inverse of Matrices and Its Applications.Wiley, New York 1971 MR 0338013 |
| Reference:
|
[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 2173229 |
| . |
