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Keywords:
minimum invariant quadratic estimators; MINQUE; mixed linear model; linear restrictions; one-way classification model
minimum invariant quadratic estimators; MINQUE; mixed linear model; linear restrictions; one-way classification model
Summary:
The MINQUE of the linear function $\int'\vartheta$ of the unknown variance-components parameter $\vartheta$ in mixed linear model under linear restrictions of the type $\bold R\vartheta = c$ 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.
References:
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[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. MR 0338013 | Zbl 0236.15005
[4] J. Seely: Linear spaces and unbiased estimation. Ann. Math. Stat. 41 (1970), 1725-1734. DOI 10.1214/aoms/1177696817 | MR 0275559 | 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. DOI 10.1214/aoms/1177698779 | MR 0214237
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