How the design of an experiment influences the nonsensitiveness regions in models with variance components

Lubomír Kubáček; Ludmila Kubáčková; Eva Tesaříková; Jaroslav Marek

Applications of Mathematics (1998)

  • Volume: 43, Issue: 6, page 439-460
  • ISSN: 0862-7940

Abstract

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Nonsensitiveness regions for estimators of linear functions, for confidence ellipsoids, for the level of a test of a linear hypothesis on parameters and for the value of the power function are investigated in a linear model with variance components. The influence of the design of an experiment on the nonsensitiveness regions mentioned is numerically demonstrated and discussed on an example.

How to cite

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Kubáček, Lubomír, et al. "How the design of an experiment influences the nonsensitiveness regions in models with variance components." Applications of Mathematics 43.6 (1998): 439-460. <http://eudml.org/doc/33020>.

@article{Kubáček1998,
abstract = {Nonsensitiveness regions for estimators of linear functions, for confidence ellipsoids, for the level of a test of a linear hypothesis on parameters and for the value of the power function are investigated in a linear model with variance components. The influence of the design of an experiment on the nonsensitiveness regions mentioned is numerically demonstrated and discussed on an example.},
author = {Kubáček, Lubomír, Kubáčková, Ludmila, Tesaříková, Eva, Marek, Jaroslav},
journal = {Applications of Mathematics},
keywords = {mixed linear model; model with variance components; nonsensitiveness region; mixed linear models; nonsensitiveness regions},
language = {eng},
number = {6},
pages = {439-460},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {How the design of an experiment influences the nonsensitiveness regions in models with variance components},
url = {http://eudml.org/doc/33020},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Kubáček, Lubomír
AU - Kubáčková, Ludmila
AU - Tesaříková, Eva
AU - Marek, Jaroslav
TI - How the design of an experiment influences the nonsensitiveness regions in models with variance components
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 6
SP - 439
EP - 460
AB - Nonsensitiveness regions for estimators of linear functions, for confidence ellipsoids, for the level of a test of a linear hypothesis on parameters and for the value of the power function are investigated in a linear model with variance components. The influence of the design of an experiment on the nonsensitiveness regions mentioned is numerically demonstrated and discussed on an example.
LA - eng
KW - mixed linear model; model with variance components; nonsensitiveness region; mixed linear models; nonsensitiveness regions
UR - http://eudml.org/doc/33020
ER -

References

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  1. The effect of stochastic relations on the statistical properties of an estimator, Contr. Geoph. Inst. Slov. Acad. Sci. 17 (1987), 31–42. (1987) 
  2. Foundations of Estimation Theory, Elsevier, Amsterdam-Oxford-New York-Tokyo, 1988. (1988) MR0995671
  3. 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. (1990) 
  4. Sensitiveness and non-sensitiveness in mixed linear models, Manuscripta geodaetica 16 (1991), 63–71. (1991) 
  5. Criterion for an approximation of variance components in regression models, Acta Universitatis Palackianae Olomucensis, Fac. rer. nat., Mathematica 34 (1995), 91–108. (1995) MR1447258
  6. Linear model with inaccurate variance components, Applications of Mathematics 41 (1996), 433–445. (1996) MR1415250
  7. Mathematical Statistics, J. Wiley & Sons, Inc., New York, London, 1962. (1962) Zbl0173.45805MR0144404

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