# Multistage regression model

Aplikace matematiky (1986)

• Volume: 31, Issue: 2, page 89-96
• ISSN: 0862-7940

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## Abstract

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Necessary and sufficient conditions are given under which the best linear unbiased estimator (BLUE) ${\stackrel{^}{\beta }}_{i}\left({Y}_{1},\cdots ,{Y}_{i}\right)$ is identical with the BLUE ${\stackrel{^}{\beta }}_{i}\left({\stackrel{^}{\beta }}_{1},\cdots ,{\stackrel{^}{\beta }}_{i-1},{Y}_{i}\right)$; ${Y}_{1}\cdots ,{Y}_{i}$ are subvectors of the random vector $Y$ in a general regression model $\left(Y,X\beta ,\sum \right)$, ${\left({\beta }_{1}^{\text{'}},\cdots ,{\beta }_{i}^{\text{'}}\right)}^{\text{'}}=\beta$ a vector of unknown parameters; the design matrix $X$ having a special so called multistage struture and the covariance matrix $\sum$ are given.

## How to cite

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Kubáček, Lubomír. "Multistage regression model." Aplikace matematiky 31.2 (1986): 89-96. <http://eudml.org/doc/15439>.

@article{Kubáček1986,
abstract = {Necessary and sufficient conditions are given under which the best linear unbiased estimator (BLUE) $\hat\{\beta \}_i(Y_1,\dots , Y_i)$ is identical with the BLUE $\hat\{\beta \}_i(\hat\{\beta \}_1,\dots , \hat\{\beta \}_\{i-1\}, Y_i)$; $Y_1\dots , Y_i$ are subvectors of the random vector $Y$ in a general regression model $(Y, X\beta ,\sum )$, $(\beta ^\{\prime \}_1,\dots ,\beta ^\{\prime \}_i)^\{\prime \}=\beta$ a vector of unknown parameters; the design matrix $X$ having a special so called multistage struture and the covariance matrix $\sum$ are given.},
author = {Kubáček, Lubomír},
journal = {Aplikace matematiky},
keywords = {mixed linear model; necessary and sufficient conditions; best linear unbiased estimator; BLUE; multistage structure; regression model; mixed linear model; Necessary and sufficient conditions; best linear unbiased estimator; BLUE; multistage structure},
language = {eng},
number = {2},
pages = {89-96},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multistage regression model},
url = {http://eudml.org/doc/15439},
volume = {31},
year = {1986},
}

TY - JOUR
AU - Kubáček, Lubomír
TI - Multistage regression model
JO - Aplikace matematiky
PY - 1986
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 2
SP - 89
EP - 96
AB - Necessary and sufficient conditions are given under which the best linear unbiased estimator (BLUE) $\hat{\beta }_i(Y_1,\dots , Y_i)$ is identical with the BLUE $\hat{\beta }_i(\hat{\beta }_1,\dots , \hat{\beta }_{i-1}, Y_i)$; $Y_1\dots , Y_i$ are subvectors of the random vector $Y$ in a general regression model $(Y, X\beta ,\sum )$, $(\beta ^{\prime }_1,\dots ,\beta ^{\prime }_i)^{\prime }=\beta$ a vector of unknown parameters; the design matrix $X$ having a special so called multistage struture and the covariance matrix $\sum$ are given.
LA - eng
KW - mixed linear model; necessary and sufficient conditions; best linear unbiased estimator; BLUE; multistage structure; regression model; mixed linear model; Necessary and sufficient conditions; best linear unbiased estimator; BLUE; multistage structure
UR - http://eudml.org/doc/15439
ER -

## References

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1. Lubomír Kubáček, Efficient estimates of points in a net constructed in stages, Studia geoph. et geod. 15, 1971, 246-253. (1971)
2. Lubomír Kubáček, Locally best quadratic estimators, Math. Slovaca 35, 1985, 393 - 408. (1985) MR0820638
3. C. R. Rao, Linear Statistical Inference and Its Applications, J. Wiley, N. York 1965. (1965) Zbl0137.36203MR0221616
4. С. R. Rao S. K. Mitra, Generalized Inverse of Matrices and Its Applications, J. Wiley, N. York 1971. (1971) MR0338013
5. Júlia Volaufová, Estimation of mean and variance in two-stage linear models, (To appear in Aplikace matematiky.)

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