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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
Summary:
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.
References:
[1] J. Kleffe: Simultaneous estimation of expectation and covariance matrix in linear models. Math. Operat. Statist., Ser. Statistics (1978) No 3, 443-478. MR 0522072 | Zbl 0415.62026
[2] L. Kubáček: Multistage regression model. Aplikace matematiky 31 (1986) No. 2, 89-96. MR 0837470
[3] J. Volaufová: Estimation of parameters of mean and variance in two-stage linear models. Aplikace matematiky 32 (1987) No. 1, 1 - 8. MR 0879324
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