Kubáček, Lubomír; Kubáčková, Ludmila Nonsensitiveness regions in universal models. (English) Zbl 0984.62040 Math. Slovaca 50, No. 2, 219-240 (2000). For a linear statistical model without conditions of regularity, unbiased estimators are computed for the expectation \(\mathbf X \beta \) or functions of it. Here, mixed models are considered and it is investigated whether estimates of the covariance structure can destroy the optimum property of the estimator for \(\mathbf X \beta \). A universal model without constraints is defined and expressions for the estimates are developed which enable to determine boundaries of nonsensitiveness regions. Also for models with constraints such regions are found. These are defined in the space of parameters of the covariance matrix of the observation vector; a shift of these parameters inside the nonsensitiveness regions does not cause any essential damage of the estimators. Reviewer: Henning Läuter (Potsdam) Cited in 1 ReviewCited in 11 Documents MSC: 62H12 Estimation in multivariate analysis 62J05 Linear regression; mixed models 62F10 Point estimation Keywords:mixed linear models; sensitiveness; models with constraints × Cite Format Result Cite Review PDF References: [1] CHATARJEE S.- HADI A. S.: Sensitivity Analysis in Linear Regression. J. Wiley, New York-Chichester-Brisbane-Toronto-Singapore, 1988. [2] KUBÁČEK L.- KUBÁČKOVÁ L.: The effect of stochastic relations on the statistical properties of an estimator. Contrib. Geoph. Inst. Slov. Acad. Sci. 17 (1987), 31-42. [3] KUBÁCEK L.: Criterion for an approximation of variance components in regression models. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 34 (1995), 91-108. · Zbl 0852.62063 [4] KUBÁCEK L.: Linear model with inaccurate variance components. Appl. Math. 41 (1996), 433-445. · Zbl 0870.62056 [5] KUBÁČEK L.- KUBÁČKOVÁ L.: Sensitiveness and non-sensitiveness in mixed linear models. Manuscripta Geodaetica 16 (1991), 63-71. [6] KUBÁČKOVÁ L.- KUBÁČEK L.- BOGNÁROVÁ M.: Effect of changes of the covariance matrix parameters on the estimates of the first order parameters. Contrib. Geoph. Inst. Slov. Acad. Sci. 20 (1990), 7-19. [7] RAO C. R.: Linear Statistical Inference and Its Applications. J. Wiley, New York, 1965. · Zbl 0137.36203 [8] RAO C. R.-MITRA S. K.: Generalized Inverse of Matrices and Its Applications. J. Wiley, New York, 1971. · Zbl 0236.15005 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.