Geodesic
Note on the estimation of parameters of the mean and the variance in $n$-stage linear models
Applications of Mathematics, Tome 33 (1988) no. 1, pp. 41-48.

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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.
DOI : 10.21136/AM.1988.104285
Classification : 62F10, 62H12, 62J05, 62J10
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 
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     author = {Volaufov\'a, J\'ulia},
     title = {Note on the estimation of parameters of the mean and the variance in $n$-stage linear models},
     journal = {Applications of Mathematics},
     pages = {41--48},
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     zbl = {0635.62067},
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104285/}
}
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Volaufová, Júlia. Note on the estimation of parameters of the mean and the variance in $n$-stage linear models. Applications of Mathematics, Tome 33 (1988) no. 1, pp. 41-48. doi : 10.21136/AM.1988.104285. http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104285/

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