\(E\)-optimal design in irregular BIBD settings. (English) Zbl 1110.62095
Summary: When the necessary conditions for a BIBD are satisfied, but no BIBD exists, there is no simple answer for the optimal design problem. This paper identifies the \(E\)-optimal information matrices for any such irregular BIBD setting when the number of treatments is no larger than 100. \(A\)- and \(D\)-optimal designs are typically not \(E\)-optimal. An \(E\)-optimal design for 15 treatments in 21 blocks of size 5 is found.
MSC:
| 62K05 | Optimal statistical designs |
| 62K10 | Statistical block designs |
| 05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |
References:
| [1] | Hanani, H., The existence and construction of balanced incomplete block designs, Ann. Statist., 32, 361-386 (1961) · Zbl 0107.36102 |
| [2] | Hedayat, A. S.; Stufken, J.; Zhang, W. G., Contingently and virtually balanced incomplete block designs and their efficiencies under various optimality criteria, Statist. Sinica, 5, 575-591 (1995) · Zbl 0828.62067 |
| [3] | Jacroux, M., On the determination and construction of \(E\)-optimal block designs with unequal number of replicates, Biometrika, 67, 661-667 (1980) · Zbl 0444.62085 |
| [4] | Jacroux, M., On the \(E\)-optimality of regular graph designs, J. R. Statist. Soc. Ser. B, 42, 205-209 (1980) · Zbl 0443.62063 |
| [5] | Kiefer, J., Construction and optimality of generalized Youdan designs, (Srivastava, J. N., A Survey of Statistical Designs and Linear Models (1975), Amsterdam: Amsterdam North-Holland), 333-353 · Zbl 0313.62057 |
| [6] | Marshall, A. W.; Olkin, I., Inequalities: Theory of Majorization and Its Applications (1979), Academic Press Inc.: Academic Press Inc. New York · Zbl 0437.26007 |
| [7] | Morgan, J. P.; Srivastav, S. K., On the type-I optimality of nearly balanced incomplete block designs with small concurrence range, Statist. Sinica, 10, 1091-1116 (2000) · Zbl 0960.62076 |
| [8] | Nandi, H. K., On the relation between certain types of tactical configurations, Bull. Calcutta Math. Soc., 37, 92-94 (1945) · Zbl 0060.31311 |
| [9] | Reck, B. H.; Morgan, J. P., Optimal design in irregular BIBD settings, J. Statist. Plann. Inference, 129, 59-84 (2005) · Zbl 1062.62140 |
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