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Linear model with inaccurate variance components. (English) Zbl 0870.62056
Summary: A linear model with approximate variance components is considered. Differences among approximate and actual values of variance components influence the proper position and the shape of confidence ellipsoids, the level of statistical tests and their power function. A procedure how to recognize whether these differences can be neglected is given in the paper.

62J05 Linear regression; mixed models
Full Text: EuDML
[1] L. Kubáček, L. Kubáčková: The effect of stochastic relations on the statistical properties of an estimator. Contr. Geoph. Inst. Slov. Acad. Sci. 17 (1987), 31-42.
[2] L. Kubáček: Foundations of Estimation Theory. Elsevier, Amsterdam-Oxford-New York-Tokyo, 1988.
[3] L. Kubáčková, L. Kubáček, M. Bognárová: Effect of changes of the covariance matrix parameters on the estimates of the first order parameters. Contr. Geoph. Inst. Slov. Acad. Sci. 20 (1990), 7-19.
[4] L. Kubáček, L. Kubáčková: Sensitiveness and non-sensitiveness in mixed linear models. Manuscripta geodaetica 16 (1991), 63-71.
[5] L. Kubáček: Criterion for an approximation of variance components in regression models. Acta Universitatis Palackianae Olomucensis, Fac. rer. nat., Mathematica 34 (1995), 91-108. · Zbl 0852.62063
[6] C. R. Rao: Linear Statistical Inference and Its Applications. J. Wiley, New York-London-Sydney, 1965. · Zbl 0137.36203
[7] C. R. Rao, S. K. Mitra: Generalized Inverse of Matrices and its Applications. J. Wiley, New York-London-Sydney-Toronto, 1971. · Zbl 0236.15004
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