Modified minimax quadratic estimation of variance components

Viktor Witkovský

Kybernetika (1998)

  • Volume: 34, Issue: 5, page [535]-543
  • ISSN: 0023-5954

Abstract

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The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.

How to cite

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Witkovský, Viktor. "Modified minimax quadratic estimation of variance components." Kybernetika 34.5 (1998): [535]-543. <http://eudml.org/doc/33386>.

@article{Witkovský1998,
abstract = {The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.},
author = {Witkovský, Viktor},
journal = {Kybernetika},
keywords = {ellipsoidal restrictions},
language = {eng},
number = {5},
pages = {[535]-543},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Modified minimax quadratic estimation of variance components},
url = {http://eudml.org/doc/33386},
volume = {34},
year = {1998},
}

TY - JOUR
AU - Witkovský, Viktor
TI - Modified minimax quadratic estimation of variance components
JO - Kybernetika
PY - 1998
PB - Institute of Information Theory and Automation AS CR
VL - 34
IS - 5
SP - [535]
EP - 543
AB - The paper deals with modified minimax quadratic estimation of variance and covariance components under full ellipsoidal restrictions. Based on the, so called, linear approach to estimation variance components, i. e. considering useful local transformation of the original model, we can directly adopt the results from the linear theory. Under normality assumption we can can derive the explicit form of the estimator which is formally find to be the Kuks–Olman type estimator.
LA - eng
KW - ellipsoidal restrictions
UR - http://eudml.org/doc/33386
ER -

References

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  9. Rao C. R., Unified theory of linear estimation, Sankhyā Ser. B 33 (1971), 371–394 (1971) Zbl0236.62048MR0319321
  10. Rao C. R., Kleffe J., Estimation of Variance Components and Applications, Statistics and Probability, Volume 3. North–Holland, Amsterdam – New York – Oxford – Tokyo 1988 Zbl0645.62073MR0933559
  11. Rao C. R., Mitra K., Generalized Inverse of Matrices and Its Applications, Wiley, New York – London – Sydney – Toronto 1971 Zbl0261.62051MR0338013
  12. Searle S. R., Casella, G., McCulloch, Ch. E., Variance Components, (Wiley Series in Probability and Mathematical Statistics.) Wiley, New York – Chichester – Brisbane – Toronto – Singapore 1992 Zbl1108.62064MR1190470
  13. Volaufová J., A brief survey on the linear methods in variance-covariance components model, In: Model–Oriented Data Analysis (W. G. Müller, H. P. Wynn, and A. A. Zhigljavsky, eds.), Physica–Verlag, Heidelberg 1993, pp. 185–196 (1993) MR1281860
  14. Volaufová J., Witkovský V., Estimation of variance components in mixed linear model, Appl. Math. 37 (1992), 139–148 (1992) 
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