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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.
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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     title = {Note on the estimation of parameters of the mean and the variance in $n$-stage linear models},
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     year = {1988},
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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

[1] J. Kleffe: Simultaneous estimation of expectation and covariance matrix in linear models. Math. Operat. Statist., Ser. Statistics (1978) No 3, 443-478. | MR | Zbl

[2] L. Kubáček: Multistage regression model. Aplikace matematiky 31 (1986) No. 2, 89-96. | MR

[3] J. Volaufová: Estimation of parameters of mean and variance in two-stage linear models. Aplikace matematiky 32 (1987) No. 1, 1 - 8. | MR

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