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On the estimation of total weight in singular spring balance weighing designs under the covariance matrix of errors $$\sigma ^ 2G$$. (English) Zbl 0707.62163
Summary: The problem of the estimation of the linear combination of weights, $$c'w$$, in a singular spring balance weighing design when the error structure takes the form $$E(ee')=\sigma^ 2G$$ has been studied. A lower bound for the variance of the estimated linear combination of weights is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The general results are applied to the case of the total of the weights. For a specified form for G, some optimum spring balance weighing designs for the estimated total weight are found.

##### MSC:
 62K10 Statistical block designs 62J05 Linear regression; mixed models
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