In this paper we study the estimation problem of individual measurements (weights) of objects in a model of chemical balance weighing design with diagonal variance - covariance matrix of errors under the restriction k₁ + k₂ < p, where k₁ and k₂ represent the number of objects placed on the right and left pans, respectively. We want all variances of estimated measurments to be equal and attaining their lower bound. We give a necessary and sufficient condition under which this lower bound is attained by the variance of each of the estimated measurements. To construct the design matrix X of the considered optimum chemical balance weighing design we use the incidence matrices of balanced bipartite weighing designs.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1054,
author = {Bronis\l aw Ceranka and Ma\l gorzata Graczyk},
title = {Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {24},
year = {2004},
pages = {215-232},
zbl = {1165.62330},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1054}
}
Bronisław Ceranka; Małgorzata Graczyk. Optimum chemical balance weighing designs with diagonal variance-covariance matrix of errors. Discussiones Mathematicae Probability and Statistics, Tome 24 (2004) pp. 215-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1054/
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