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calibration problem; multiple-use calibration
Professor Lubomír Kubáček has provided exceptional contributions to mathematical statistics and its applications. Because of his excellent knowledge in mathematical statistics as well as in the different fields of natural and especially technical sciences, he contributed to solution of a large number of real world problems. The continuation of Professor Kubáček’s scientific work and his scientific school is demonstrated by the results of his numerous students. Here we present just one illustration of Professor Kubáček’s original research and its extension by his followers, namely, the calibration problem.
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[2] Casella, G., Berger, R. L.: Statistical Inference. Duxbury Advanced Series, Belmont, 1990. MR 1051420 | Zbl 0699.62001
[3] Eisenhart, C.: The interpretation of certain regression methods and their use in biological and industrial research. Annals of Mathematical Statistics 10 (1939), 162–186. DOI 10.1214/aoms/1177732214 | Zbl 0022.24901
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[5] Krutchkoff, R. G.: Classical and inverse methods of calibration. Technometrics 9 (1967), 425–439. DOI 10.1080/00401706.1967.10490486 | MR 0215481
[6] Kubáček, L.: Foundations of Estimation Theory. Elsevier, Amsterdam–Oxford–New York–Tokyo, 1988.
[7] Kubáček, L.: Nonlinear error propagation law. Applications of Mathematics 41 (1996), 329–345. MR 1404545
[8] Kubáček, L., Kubáčková, L.: Statistics and Metrology. Vyd. University Palackého, Olomouc, 2008, (in Czech).
[9] Kubáček, L., Kubáčková, L.: One of the calibration problems. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 36 (1997), 117–130. MR 1620541
[10] Rao, C. R., Kleffe J.: Estimation of Variance Components and Applications. North-Holland, Amsterdam–New York–Oxford–Tokyo, 1988. MR 0933559 | Zbl 0645.62073
[11] Scheffé, H.: The Analysis of Variance. Wiley, New York, 1959. MR 0116429
[12] Scheffé, H.: A statistical theory of calibration. The Annals of Statistics 1 (1973), 1–37. DOI 10.1214/aos/1193342379 | MR 0336920
[13] Wimmer, G., Witkovský, V.: Univariate linear calibration via error in variables model. Journal of Statistical Computation and Simulation 77 (2007), 213–227. DOI 10.1080/10629360600679433 | MR 2345730
[14] Wimmer, G., Witkovský, V., Savin, A.: Confidence region for parameters in replicated errors in variables model. In: Antoch, J. (ed.) Proceedings in Computational Statistics, 16th Syposium, Prague, Czech Republic, Physica-Verlag, 2004, 1987–1994. MR 2173229
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