Abstract
The paper deals with the problem of estimating the weights of objects using an A-optimal chemical balance weighing design with the covariance matrix of errors o2G, where G is an n x n known positive definite diagonal matrix. A lower bound of tr(X’G-1X)-1is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The incidence matrices of balanced incomplete block designs have been used to construct A-optimal chemical balance weighing designs.
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