The paper deals with the estimation of unknown vector parameter of mean and scalar parameters of variance as well in two-stage linear model, which is a special type of mixed linear model. The necessary and sufficient condition for the existence of uniformly best unbiased estimator of parameter of means is given. The explicite formulas for these estimators and for the estimators of the parameters of variance as well are derived.
@article{104230,
author = {J\'ulia Volaufov\'a},
title = {Estimation of parameters of mean and variance in two-stage linear models},
journal = {Applications of Mathematics},
volume = {32},
year = {1987},
pages = {1-8},
zbl = {0616.62091},
mrnumber = {0879324},
language = {en},
url = {http://dml.mathdoc.fr/item/104230}
}
Volaufová, Júlia. Estimation of parameters of mean and variance in two-stage linear models. Applications of Mathematics, Tome 32 (1987) pp. 1-8. http://gdmltest.u-ga.fr/item/104230/
Simultaneous estimation of expectation and covariance matrix in linear models, Math. Oper. Stat. Ser. Stat., No 3, Vol 9 (1978), 443-478. (1978) | MR 0522072 | Zbl 0415.62026
, Private communication.
Efficient estimates of points in a net constructed in stages, Studia geoph. et geod., 15 (1971), 246-253. (1971)
Linear statistical inference and its applications, John Wiley, New York, 1973. (1973) | MR 0346957 | Zbl 0256.62002
Estimation of variance and covariance components - MINQUE-theory, J. Multiv. Anal., 1 (1971), 257-275. (1971) | Article | MR 0301869 | Zbl 0223.62086
Estimation of variance components, P. R. Krishnaiah, ed. Handbook of Statistics. Vol 1, North Holl. Publ. Соmр., 1 - 40.