# Note on the estimation of parameters of the mean and the variance in $n$-stage linear models

Aplikace matematiky (1988)

- Volume: 33, Issue: 1, page 41-48
- ISSN: 0862-7940

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topVolaufová, Júlia. "Note on the estimation of parameters of the mean and the variance in $n$-stage linear models." Aplikace matematiky 33.1 (1988): 41-48. <http://eudml.org/doc/15522>.

@article{Volaufová1988,

abstract = {The paper deals with the estimation of the unknown vector parameter of the mean and the parameters of the variance in the general $n$-stage linear model. Necessary and sufficient conditions for the existence of the uniformly minimum variance unbiased estimator (UMVUE) of the mean-parameter under the condition of normality are given. The commonly used least squares estimators are used to derive the expressions of UMVUE-s in a simple form.},

author = {Volaufová, Júlia},

journal = {Aplikace matematiky},

keywords = {general $n$-stage linear model; necessary and sufficient conditions; existence of the uniformly minimum variance unbiased estimator; mean parameter; condition of normality; least squares estimators; general n-stage linear model; Necessary and sufficient conditions; existence of the uniformly minimum variance unbiased estimator; mean- parameter; condition of normality; least squares estimators},

language = {eng},

number = {1},

pages = {41-48},

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

title = {Note on the estimation of parameters of the mean and the variance in $n$-stage linear models},

url = {http://eudml.org/doc/15522},

volume = {33},

year = {1988},

}

TY - JOUR

AU - Volaufová, Júlia

TI - Note on the estimation of parameters of the mean and the variance in $n$-stage linear models

JO - Aplikace matematiky

PY - 1988

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

VL - 33

IS - 1

SP - 41

EP - 48

AB - The paper deals with the estimation of the unknown vector parameter of the mean and the parameters of the variance in the general $n$-stage linear model. Necessary and sufficient conditions for the existence of the uniformly minimum variance unbiased estimator (UMVUE) of the mean-parameter under the condition of normality are given. The commonly used least squares estimators are used to derive the expressions of UMVUE-s in a simple form.

LA - eng

KW - general $n$-stage linear model; necessary and sufficient conditions; existence of the uniformly minimum variance unbiased estimator; mean parameter; condition of normality; least squares estimators; general n-stage linear model; Necessary and sufficient conditions; existence of the uniformly minimum variance unbiased estimator; mean- parameter; condition of normality; least squares estimators

UR - http://eudml.org/doc/15522

ER -

## References

top- J. Kleffe, Simultaneous estimation of expectation and covariance matrix in linear models, Math. Operat. Statist., Ser. Statistics (1978) No 3, 443-478. (1978) Zbl0415.62026MR0522072
- L. Kubáček, Multistage regression model, Aplikace matematiky 31 (1986) No. 2, 89-96. (1986) MR0837470
- J. Volaufová, Estimation of parameters of mean and variance in two-stage linear models, Aplikace matematiky 32 (1987) No. 1, 1 - 8. (1987) MR0879324

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