Linear model with inaccurate variance components

Lubomír Kubáček

Applications of Mathematics (1996)

  • Volume: 41, Issue: 6, page 433-445
  • ISSN: 0862-7940

Abstract

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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 diferences can be neglected is given in the paper.

How to cite

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Kubáček, Lubomír. "Linear model with inaccurate variance components." Applications of Mathematics 41.6 (1996): 433-445. <http://eudml.org/doc/32960>.

@article{Kubáček1996,
abstract = {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 diferences can be neglected is given in the paper.},
author = {Kubáček, Lubomír},
journal = {Applications of Mathematics},
keywords = {mixed linear model; linear model with variance components; mixed linear model; linear model with variance components},
language = {eng},
number = {6},
pages = {433-445},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear model with inaccurate variance components},
url = {http://eudml.org/doc/32960},
volume = {41},
year = {1996},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - Linear model with inaccurate variance components
JO - Applications of Mathematics
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 41
IS - 6
SP - 433
EP - 445
AB - 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 diferences can be neglected is given in the paper.
LA - eng
KW - mixed linear model; linear model with variance components; mixed linear model; linear model with variance components
UR - http://eudml.org/doc/32960
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 Statistical Inference and Its Applications, J. Wiley, New York-London-Sydney, 1965. (1965) Zbl0137.36203MR0221616
  7. Generalized Inverse of Matrices and its Applications, J. Wiley, New York-London-Sydney-Toronto, 1971. (1971) MR0338013

Citations in EuDML Documents

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  1. Eva Lešanská, Optimization of the size of nonsensitiveness regions
  2. Eva Fišerová, Lubomír Kubáček, Sensitivity analysis in singular mixed linear models with constraints
  3. Lubomír Kubáček, Ludmila Kubáčková, Nonsensitiveness regions in universal models
  4. Lubomír Kubáček, Ludmila Kubáčková, Eva Tesaříková, Jaroslav Marek, How the design of an experiment influences the nonsensitiveness regions in models with variance components
  5. Lubomír Kubáček, Eva Tesaříková, Variance components and nonlinearity
  6. Eva Lešanská, Nonsensitiveness regions for threshold ellipsoids
  7. Lubomír Kubáček, Some remarks to multivariate regression model
  8. Lubomír Kubáček, Multivariate regression model with constraints
  9. Lubomír Kubáček, Multivariate statistical models; solvability of basic problems

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