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

Júlia Volaufová

Aplikace matematiky (1987)

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

Abstract

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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.

How to cite

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Volaufová, 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

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  1. 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
  2. J. Krč-Jediný, [unknown], Private communication. 
  3. L. Kubáček, Efficient estimates of points in a net constructed in stages, Studia geoph. et geod., 15 (1971), 246-253. (1971) 
  4. C. R. Rao, Linear statistical inference and its applications, John Wiley, New York, 1973. (1973) Zbl0256.62002MR0346957
  5. 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
  6. C. R. Rao J. Kleffe, Estimation of variance components, P. R. Krishnaiah, ed. Handbook of Statistics. Vol 1, North Holl. Publ. Соmр., 1 - 40. Zbl0476.62058

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