# zbMATH — the first resource for mathematics

Multistage regression model. (English) Zbl 0595.62062
Summary: Necessary and sufficient conditions are given under which the best linear unbiased estimator (BLUE) $${\hat \beta}_ i(Y_ 1,...,Y_ i)$$ is identical with the BLUE $${\hat \beta}_ i({\hat \beta}_ 1,...,{\hat \beta}_{i-1},Y_ i);$$ $$Y_ 1,...,Y_ i$$ are subvectors of the random vector Y in a general regression model (Y,X$$\beta$$,$$\Sigma)$$, $$(\beta_ 1',...,\beta_ i')'=\beta$$ a vector of unknown parameters. The design matrix X having a special so called multistage structure and the covariance matrix $$\Sigma$$ are given.

##### MSC:
 62J05 Linear regression; mixed models
Full Text:
##### References:
 [1] Lubomír Kubáček: Efficient estimates of points in a net constructed in stages. Studia geoph. et geod. 15, 1971, 246-253. [2] Lubomír Kubáček: Locally best quadratic estimators. Math. Slovaca 35, 1985, 393 - 408. · Zbl 0597.62050 [3] C. R. Rao: Linear Statistical Inference and Its Applications. J. Wiley, N. York 1965. · Zbl 0137.36203 [4] C. R. Rao S. K. Mitra: Generalized Inverse of Matrices and Its Applications. J. Wiley, N. York 1971. · Zbl 0236.15004 [5] Júlia Volaufová: Estimation of mean and variance in two-stage linear models. · Zbl 0616.62091
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.