Estimation of variance components in mixed linear models
Volaufová, Júlia ; Witkovský, Viktor
Applications of Mathematics, Tome 37 (1992), p. 139-148 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1992-01-01
Classification:  62F10,  62J05,  62J10
@article{104497,
     author = {J\'ulia Volaufov\'a and Viktor Witkovsk\'y},
     title = {Estimation of variance components in mixed linear models},
     journal = {Applications of Mathematics},
     volume = {37},
     year = {1992},
     pages = {139-148},
     zbl = {0746.62066},
     mrnumber = {1149163},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104497}
}
Volaufová, Júlia; Witkovský, Viktor. Estimation of variance components in mixed linear models. Applications of Mathematics, Tome 37 (1992) pp. 139-148. http://gdmltest.u-ga.fr/item/104497/

C. R. Rao Estimation of variance and covariance components - MINQUE theory, Journal of Multivariate Analysis 1 (1971), 267-275. (1971) | MR 0301869 | Zbl 0223.62086

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. (1988) | MR 0933559 | Zbl 0645.62073

C. R. Rao; S. K. Mitra Generalized Inverse of Matrices and Its Applications, John Wiley & Sons, New York, London, Sydney, Toronto, 1971, first edition. (1971) | MR 0338013 | Zbl 0236.15005

J. Seely Linear spaces and unbiased estimation, Ann. Math. Stat. 41 (1970), 1725-1734. (1970) | MR 0275559 | Zbl 0263.62041

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. (1979)

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. (1967) | MR 0214237