D-optimal and highly D-efficient designs with non-negatively correlated observations

Katulska, K.; Smaga, Łukasz

doi:10.14736/kyb-2016-4-0575

Cited by 1 publication

(2 citation statements)

References 25 publications

(38 reference statements)

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“…We do not know how to prove this, but we have confirmed it numerically. More precisely, we conducted a numerical search based on the tabu-search algorithm (Harman et al, 2016;Jung and Yum, 1996) to find the D-optimal designs in D (n, m, b) for certain n, m and k. We used a modification of the R code of a tabusearch-based approach for chemical balance weighing designs by Katulska and Smaga (2016) (Domijan, 2012;R Core Team, 2015). It is significant that we did not find D-better designs than d 4 .…”

Section: D-optimal Designs Whenmentioning

confidence: 99%

“…It can be modified for other experimental designs and other optimality criteria, since it is usually quite easy to obtain a lower or upper (depending on the criterion) bound for the value of a criterion (see, for example, Katulska and Smaga, 2016). Studying efficiency in this way, may help to indicate very good or even optimal designs under a given optimality criterion.…”

Section: D-optimal Designs Whenmentioning

confidence: 99%

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A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans

Smaga

2016

Biometrical Letters

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SummaryThis 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.

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Section: D-optimal Designs Whenmentioning

confidence: 99%

Section: D-optimal Designs Whenmentioning

confidence: 99%