×
Kubáček, Lubomír

Problems of an additional experiment. (English) Zbl 1197.62076

Math. Slovaca 57, No. 1, 59-82 (2007).
Summary: In some situations the estimates of the unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulas for the correction itself. These formulas enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations.

MSC:

62J05 Linear regression; mixed models
62J20 Diagnostics, and linear inference and regression

Keywords:

mixed linear models; variance components
Cite Review PDF
Full Text: DOI Link
Creative Commons CC license icon Creative Commons BY license icon Creative Commons NC license icon Creative Commons ND license icon

References:

[1] DIGGLE P. J.-LIANG K.-Y.-ZEGER S. L.: Analysis of Longitudinal Data. Oxford Science Publications, Oxford, 1994.
[2] FIŠEROVÁ E.-KUBÁCEK L.: Sensitivity analysis in singular mixed linear models with constraints. Kybernetika (Prague) 39 (2003), 317-332. · Zbl 1248.62112
[3] HUMAK K. M. S.: Statistische Methoden der Modellbildung. Band I. Akademie-Verlag, Berlin, 1977. · Zbl 0353.62001
[4] KUBÁČEK L.-KUBÁČKOVÁ L.-VOLAUFOVÁ J.: Statistical Models with Linear Structures. Veda, Bratislava, 1995.
[5] KUBÁCEK L.-KUBÁČKOVÁ L.: Nonsensitiveness regions in universal models. Math. Slovaca 50 (2000), 219-240. · Zbl 0984.62040
[6] KUBÁČEK L.-KUBÁČKOVÁ L.: Statistics and Metrology. Publishing House of Palacký University Olomouc, Olomouc 2000
[7] KUBÁČEK L.-FIŠEROVÁ E.: Problems of sensitiveness and linearization in a detruination of isobestic points. Math. Slovaca 53 (2003), 407-426. · Zbl 1070.62057
[8] KUBÁČEK L.-FIŠEROVÁ E.: Isobestic points: sensitiveness and linearization. Tatra Mt. Math. Publ. 26 (2003), 1-10. · Zbl 1065.62118
[9] LEŠANSKÁ E.: Insensitivity regions for estimators of mean value parameters in mixed models with constraints. Tatra Mt. Math. Publ. 22 (2001), 37-49. · Zbl 1001.62012
[10] LEŠANSKÁ E.: Insensitivity regions for testing hypotheses in mixed models with constraints. Tatra Mt. Math. Publ. 22 (2001), 209-222. · Zbl 1001.62011
[11] LEŠANSKÁ E.: Optimization of the size of nonsensitiveness regions. Appl. Math. 47 (2002), 9-23.
[12] LEŠANSKÁ E.: Nonsensitiveness regions for threshold ellipsoids. Appl. Math. 47 2002 , 411-426. · Zbl 1091.62518 · doi:10.1023/A:1021761924588
[13] RAO C. R.: Linear Statistical Inference and Its Applications. J. Wiley & Sons, New York-London-Sydney, 1965. · Zbl 0137.36203
[14] RAO C. R.-MITRA S. K.: Generalized Inverse of Matrices and Its Applications. John Wiley & Sons, New York-London-Sydney-Toronto, 1971. · Zbl 0236.15005
[15] RAO C. R.-KLEFFE J.: Estimation of Variance Components and Applicatpons. North-Holland, Amsterdam, 1988. · Zbl 0645.62073
[16] SCHEFFÉ H.: The Analysis of Variance. J. Wiley, New York, 1959. · Zbl 0086.34603
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.