Previous |  Up |  Next

Article

Keywords:
additional experiment; variance components; insensitivity region
Summary:
Estimators of parameters of an investigated object can be considered after some time as insufficiently precise. Therefore, an additional measurement must be realized. A model of a measurement, taking into account both the original results and the new ones, has a litle more complicated covariance matrix, since the variance components occur in it. How to deal with them is the aim of the paper.
References:
[1] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models; Regularity and Singularities. Academia Praha (2007).
[2] Chatterjee, S., Hadi, A. S.: Sensitivity Analysis in Linear Regression. J. Wiley New York (1988). MR 0939610 | Zbl 0648.62066
[3] Giles, D. E. A., Srivastava, V. K.: An unbiased eastimator of the covariance matrix of the mixed regression estimator. J. Am. Stat. Assoc. 86 (1991), 441-444 \MR 1137127. DOI 10.1080/01621459.1991.10475063 | MR 1137127
[4] Kubáček, L., Kubáčková, L., Volaufová, J.: Statistical Models with Linear Structures. Veda Bratislava (1995).
[5] Kubáček, L., Kubáčková, L.: Nonsensitiveness regions in universal models. Math. Slovaca 50 (2000), 219-240. MR 1763121
[6] Kubáček, L., Kubáčková, L.: Statistics and Metrology. Publishing House of Palacký University Olomouc (2000), Czech.
[7] Neter, J., Wassermann, W., Kutner, M. H.: Applied Linear Statistical Models, 3rd edition. Irwin Boston (1990).
[8] Rao, C. R.: Unified theory of least squares. Commun. Stat., Part A---Theory and Methods 1 (1973), 1-8. DOI 10.1080/03610927208827002 | MR 0315850 | Zbl 0252.62037
[9] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications. John Wiley & Sons New York-London-Sydney-Toronto (1971). MR 0338013 | Zbl 0236.15005
[10] Rao, C. R.: Linear Statistical Inference and Its Applications. John Wiley & Sons New York-London-Sydney (1973); Czech translation: Academia, Praha, 1978. MR 0221616 | Zbl 0256.62002
[11] Rao, C. R., Kleffe, J.: Estimation of Variance Components and Applications. North-Holland Amsterdam-New York-Oxford-Tokyo (1988). MR 0933559 | Zbl 0645.62073
[12] Rao, C. R., Toutenburg, H.: Linear Models. Least Squares and Alternatives, 2nd ed. Springer New York (1999). MR 1707290
[13] Seber, G. A. F., Lee, A. J.: Linear Regression Analysis, 2nd ed. Wiley New York (2003) \MR 0958247. MR 1958247 | Zbl 1029.62059
[14] Weisberg, S.: Applied Linear Regression, 3rd revised ed. John Wiley & Sons New York (1980). MR 0591462
Partner of
EuDML logo