One of the calibration problems. (English) Zbl 0959.62052

Summary: Two measurement devices are characterized by dispersions \(\sigma^2_1\) and \(\sigma^2_2\) of their registration. The ratio \(\sigma^2_1/\sigma^2_2\) is a priori unknown and approximations \(\sigma^2_{1,0}\) and \(\sigma^2_{2,0}\) are at our disposal only. The relation between errorless registrations of these devices is given by the calibration curve.
One of the procedures of constructing this curve is described in this paper. Futher, accuracy characteristics of the calibration curve parameters estimators and the MINQUE \(\widehat\sigma^2_1\) and \(\widehat\sigma^2_2\) of the dispersions \(\sigma^2_1\) and \(\sigma^2_2\) are given.


62H12 Estimation in multivariate analysis
62J99 Linear inference, regression
62J05 Linear regression; mixed models
62F10 Point estimation


[1] Kubáček L.: Nonlinear error propagation law. Appl. of Math. 41 (1996), 329-345. · Zbl 0870.62017
[2] Kubáčková L.: Foundations of Experimental Data Analysis. CRC Press, Boca Raton-Ann Arbor-London-Tokyo 1992. · Zbl 0875.62016
[3] Rao C. R., Mitra K. S.: Generalized Inverse of Matrices and Its Application. J. Wiley, New York-London-Sydney-Toronto, 1971. · Zbl 0236.15004
[4] Rao C. R., Kleffe J.: Estimation of Variance Components and Applications. North-Holland, Amsterdam-Oxford-New York-Tokyo 1988. · Zbl 0645.62073
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.