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Some D-optimal chemical balance weighing designs: theory and examples

100%
Ceranka B., Graczyk M.
Biometrical Letters
|
2017
|
tom 54
|
nr 2
137-154
EN
In this paper we study a certain kind of experimental designs called chemical balance weighing designs. We consider issues with regard to determining optimality conditions. We give new classes of designs in which we are able to determine an optimal design. Moreover, examples are given for the presented cases.
2
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A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans

61%
Smaga Ł.
Biometrical Letters
|
2016
|
tom 53
|
nr 2
119-131
EN
This paper considers main effects plans used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. The assumptions are adopted that n ≡ 2 (mod 8) and k > 2 is even. Certain designs not having all main effects orthogonal to blocks were shown by Jacroux (2011a) to be D-optimal when (m − 2)(k − 2) + 2 ⩽ n ⩽ (m − 1)(k − 2) + 2. Here, we extend that result. For (m − 3)(k − 2) + 2 ⩽ n < (m − 2)(k − 2) + 2, the D-optimality of those designs is proved. Moreover, their D-efficiency is shown to be close to one for 2(m + 1) ⩽ n < (m − 3)(k − 2) + 2, indicating their good performance under the criterion of D-optimality.
3
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On optimality of the orthogonal block design

61%
Synówka-Bejenka E., Zontek S.
Discussiones Mathematicae Probability and Statistics
|
2012
|
tom 32
|
nr 1-2
59-68
EN
In the paper a usual block design with treatment effects fixed and block effects random is considered. To compare experimental design the asymptotic covariance matrix of a robust estimator proposed by Bednarski and Zontek (1996) for simultaneous estimation of shift and scale parameters is used. Asymptotically A- and D- optimal block designs in the class of designs with bounded block sizes are characterized.
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