# Multistage regression model

Aplikace matematiky (1986)

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

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topKubáček, 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

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

## Citations in EuDML Documents

top- Júlia Volaufová, Note on the estimation of parameters of the mean and the variance in $n$-stage linear models
- Lubomír Kubáček, Two-stage regression model
- Marta Bognárová, Lubomír Kubáček, Júlia Volaufová, Comparison of MINQUE and LMVQUIE by simulation
- Lubomír Kubáček, Two stage linear model with constraints

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