On the estimation of total weight in singular spring balance weighing designs under the covariance matrix of errors \(\sigma ^ 2G\). (English) Zbl 0707.62163

Katulska, Krystyna

Aust. J. Stat. 31, No. 2, 277-286 (1989).

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

Keywords:

block design; optimum singular spring balance weighing design