Lešanská, Eva Nonsensitiveness regions for threshold ellipsoids. (English) Zbl 1091.62518 Appl. Math., Praha 47, No. 5, 411-426 (2002). Threshold region in a mixed linear statistical model is defined as a set in parametric space. On the boundary of this set the power function of the test of a linear hypothesis on the model parameters attains the prescribed value (near to 1). In the case of normality the shape of this set is an ellipsoid. Position and a size of the threshold ellipsoid depends on the values of the covariance matrix parameters. Nonsensitiveness region is such a neighbourhood of a given covariance matrix vector parameter that for points of its interior the value of the power function is larger than the prescribed value minus sufficient small number. The boundary of the nonsensitiveness region is determined in the paper. Reviewer: Lubomír Kubáček (Olomouc) Cited in 2 Documents MSC: 62H15 Hypothesis testing in multivariate analysis 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62J05 Linear regression; mixed models Keywords:mixed linear model; power function; threshold ellipsoid; nonsensitiveness region × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link References: [1] J. Janko: Statistical Tables. Academia, Praha, 1958. [2] L. Kubáček: Criterion for approximation of variance components in regression models. Acta Univ. Palack. Olomouc. Fac. Rerum Natur. Math. 34 (1995), 91-108. · Zbl 0852.62063 [3] L. Kubáček: Linear model with inaccurate variance components. Appl. Math. 41 (1996), 433-445. · Zbl 0870.62056 [4] L. Kubáček, L. Kubáčková: Nonsensitiveness regions in universal models. Math. Slovaca 50 (2000), 219-240. · Zbl 0984.62040 [5] L. Kubáček, L. Kubáčková, E. Tesaříková and J. Marek: How the design of an experiment influences the nonsensitiveness regions in models with variance components. Appl. Math. 43 (1998), 439-460. · Zbl 0937.62070 · doi:10.1023/A:1023269321385 [6] L. Kubáčková: Joint confidence and threshold ellipsoids in regression models. Tatra Mt. Math. Publ. 7 (1996), 157-160. · Zbl 0925.62284 [7] E. Lešanská: Optimization of the size of nonsensitiveness regions. Appl. Math. 47 (2002), 9-23. · Zbl 1091.62521 · doi:10.1023/A:1021750700055 [8] C. R. Rao: Statistical Inference and Its Applications. J. Wiley, New York-London-Sydney, 1965. · Zbl 0137.36203 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.