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

top
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

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.