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D-optimal and highly D-efficient designs with non-negatively correlated observations
Kybernetika, Tome 52 (2016) no. 4, pp. 575-588 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be highly D-efficient. Theoretical results are accompanied by numerical search, suggesting D-optimality of designs under consideration.
In this paper we consider D-optimal and highly D-efficient chemical balance weighing designs. The errors are assumed to be equally non-negatively correlated and to have equal variances. Some necessary and sufficient conditions under which a design is D*-optimal design (regular D-optimal design) are proved. It is also shown that in many cases D*-optimal design does not exist. In many of those cases the designs constructed by Masaro and Wong (2008) and some new designs are shown to be highly D-efficient. Theoretical results are accompanied by numerical search, suggesting D-optimality of designs under consideration.
DOI : 10.14736/kyb-2016-4-0575
Classification : 15A18, 62K05
Keywords: correlation; D-efficiency; D-optimal chemical balance weighing design; Hadamard matrix; simulated annealing algorithm; tabu search 
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Katulska, Krystyna; Smaga, Łukasz. D-optimal and highly D-efficient designs with non-negatively correlated observations. Kybernetika, Tome 52 (2016) no. 4, pp. 575-588. doi: 10.14736/kyb-2016-4-0575

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