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Note on the estimation of parameters of the mean and the variance in n- stage linear models. (English) Zbl 0635.62067
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.

MSC:
62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
62F10 Point estimation
62J10 Analysis of variance and covariance (ANOVA)
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References:
[1] J. Kleffe: Simultaneous estimation of expectation and covariance matrix in linear models. Math. Operat. Statist., Ser. Statistics (1978) No 3, 443-478. · Zbl 0415.62026
[2] L. Kubáček: Multistage regression model. Aplikace matematiky 31 (1986) No. 2, 89-96. · Zbl 0595.62062
[3] J. Volaufová: Estimation of parameters of mean and variance in two-stage linear models. Aplikace matematiky 32 (1987) No. 1, 1 - 8. · Zbl 0616.62091
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