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Volaufová, Júlia; Witkovský, Viktor

Estimation of variance components in mixed linear models. (English) Zbl 0746.62066

Appl. Math., Praha 37, No. 2, 139-148 (1992).
Summary: The MINQUE of the linear function \(f'\vartheta\) of the unknown variance- components parameter \(\vartheta\) in mixed linear model under linear restrictions of the type \(R\vartheta=c\) is defined and derived. As an illustration of this estimator the example of the one-way classification model with the restrictions \(\vartheta_ 1=k\vartheta_ 2\), where \(k\geq 0\), is given.

Cited in 3 Documents

MSC:

62J10 Analysis of variance and covariance (ANOVA)
62F10 Point estimation
62J05 Linear regression; mixed models

Keywords:

minimum invariant quadratic estimators; MINQUE; mixed linear model; linear restrictions; one-way classification model
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\textit{J. Volaufová} and \textit{V. Witkovský}, Appl. Math., Praha 37, No. 2, 139--148 (1992; Zbl 0746.62066)
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References:

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[2] C. R. Rao, J. Kleffe: Estimation of Variance Components and Applications. volume 3 of Statistics and probability, North-Holland, Amsterdam, New York, Oxford, Tokyo, 1988, first edition. · Zbl 0645.62073
[3] C. R. Rao, S. K. Mitra: Generalized Inverse of Matrices and Its Applications. John Wiley & Sons, New York, London, Sydney, Toronto, 1971, first edition. · Zbl 0236.15005
[4] J. Seely: Linear spaces and unbiased estimation. Ann. Math. Stat. 41 (1970), 1725-1734. · Zbl 0263.62041
[5] L. R. Verdooren: Practical aspects of variance component estimation. invited lecture for the 4th International Summer School on Problems of Model Choice and Parameter Estimation in Regression Analysis Mülhausen, GDR, May 1979.
[6] G. Zyskind: On canonical forms, negative covariance matrices and best and simple least square estimator in linear models. Ann. Math. Stat. 38 (1967), 1092-1110. · Zbl 0171.17103
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.