vector parameter; mean; variance; two-stage linear model; mixed linear model; necessary and sufficient condition; existence; uniformly best unbiased estimator
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.
 J. Kleffe: Simultaneous estimation of expectation and covariance matrix in linear models
. Math. Oper. Stat. Ser. Stat., No 3, Vol 9 (1978), 443-478. MR 0522072
| Zbl 0415.62026
 J. Krč-Jediný: Private communication.
 L. Kubáček: Efficient estimates of points in a net constructed in stages. Studia geoph. et geod., 15 (1971), 246-253.
 C. R. Rao: Linear statistical inference and its applications
. John Wiley, New York, 1973. MR 0346957
| Zbl 0256.62002
 C. R. Rao J. Kleffe: Estimation of variance components. P. R. Krishnaiah, ed. Handbook of Statistics. Vol 1, North Holl. Publ. Соmр., 1 - 40.