Optimal design in irregular BIBD settings. (English) Zbl 1062.62140
Summary: When the necessary conditions for a balanced incomplete block design (BIBD) are satisfied, but no BIBD exists, there is no simple answer for the optimal design problem. In such an irregular BIBD setting, identification of an A-optimal or D-optimal design requires a delicate interplay of combinatorics and optimality tools.
Here the known theory is extended, giving a more comprehensive picture of the set of potentially optimal designs and affording a better understanding of the relationship between optimality and simple combinatorial measures of symmetry. The theory in conjunction with an intricate search leads to the A- and D-optimal design for \(D\)(15,21,5); this is the first known optimal design for an irregular BIBD setting. Insight is also gained on resolvable members of \(D\)(15,21,5).
Here the known theory is extended, giving a more comprehensive picture of the set of potentially optimal designs and affording a better understanding of the relationship between optimality and simple combinatorial measures of symmetry. The theory in conjunction with an intricate search leads to the A- and D-optimal design for \(D\)(15,21,5); this is the first known optimal design for an irregular BIBD setting. Insight is also gained on resolvable members of \(D\)(15,21,5).
MSC:
| 62K05 | Optimal statistical designs |
| 05B05 | Combinatorial aspects of block designs |
| 62K10 | Statistical block designs |
Keywords:
Balanced incomplete block design; Treatment discrepancy; Treatment deficiency; Unfinished design; A-optimality; tablesReferences:
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