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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
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.
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