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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
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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
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[5] Júlia Volaufová: Estimation of mean and variance in two-stage linear models. · Zbl 0616.62091
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