# Estimation of parameters of mean and variance in two-stage linear models

Aplikace matematiky (1987)

- Volume: 32, Issue: 1, page 1-8
- ISSN: 0862-7940

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topVolaufová, Júlia. "Estimation of parameters of mean and variance in two-stage linear models." Aplikace matematiky 32.1 (1987): 1-8. <http://eudml.org/doc/15474>.

@article{Volaufová1987,

abstract = {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.},

author = {Volaufová, Júlia},

journal = {Aplikace matematiky},

keywords = {vector parameter; mean; variance; two-stage linear model; mixed linear model; necessary and sufficient condition; existence; uniformly best unbiased estimator; vector parameter; mean; variance; two-stage linear model; mixed linear model; necessary and sufficient condition; existence; uniformly best unbiased estimator},

language = {eng},

number = {1},

pages = {1-8},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Estimation of parameters of mean and variance in two-stage linear models},

url = {http://eudml.org/doc/15474},

volume = {32},

year = {1987},

}

TY - JOUR

AU - Volaufová, Júlia

TI - Estimation of parameters of mean and variance in two-stage linear models

JO - Aplikace matematiky

PY - 1987

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 32

IS - 1

SP - 1

EP - 8

AB - 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.

LA - eng

KW - vector parameter; mean; variance; two-stage linear model; mixed linear model; necessary and sufficient condition; existence; uniformly best unbiased estimator; vector parameter; mean; variance; two-stage linear model; mixed linear model; necessary and sufficient condition; existence; uniformly best unbiased estimator

UR - http://eudml.org/doc/15474

ER -

## References

top- J. Kleffe, Simultaneous estimation of expectation and covariance matrix in linear models, Math. Oper. Stat. Ser. Stat., No 3, Vol 9 (1978), 443-478. (1978) Zbl0415.62026MR0522072
- J. Krč-Jediný, [unknown], Private communication.
- L. Kubáček, Efficient estimates of points in a net constructed in stages, Studia geoph. et geod., 15 (1971), 246-253. (1971)
- C. R. Rao, Linear statistical inference and its applications, John Wiley, New York, 1973. (1973) Zbl0256.62002MR0346957
- C. R. Rao, 10.1016/0047-259X(71)90001-7, J. Multiv. Anal., 1 (1971), 257-275. (1971) Zbl0223.62086MR0301869DOI10.1016/0047-259X(71)90001-7
- C. R. Rao J. Kleffe, Estimation of variance components, P. R. Krishnaiah, ed. Handbook of Statistics. Vol 1, North Holl. Publ. Соmр., 1 - 40.

## 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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