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September, 1991 Optimality of Some Two-Associate-Class Partially Balanced Incomplete-Block Designs
C.-S. Cheng, R. A. Bailey
Ann. Statist. 19(3): 1667-1671 (September, 1991). DOI: 10.1214/aos/1176348270


Let $\mathscr{D}_{\upsilon,b,k}$ be the set of all the binary equireplicate incomplete-block designs for $\upsilon$ treatments in $b$ blocks of size $k$. It is shown that if $\mathscr{D}_{\upsilon,b,k}$ contains a connected two-associate-class partially balanced design $d^\ast$ with $\lambda_2 = \lambda_1 \pm 1$ which has a singular concurrence matrix, then it is optimal over $\mathscr{D}_{\upsilon,b,k}$ with respect to a large class of criteria including the $A,D$ and $E$ criteria. The dual of $d^\ast$ is also optimal over $\mathscr{D}_{b,\upsilon,r}$ with respect to the same criteria, where $r = bk/\upsilon$. The result can be applied to many designs which were not previously known to be optimal. In another application, Bailey's (1988) conjecture on the optimality of Trojan squares over semi-Latin squares is confirmed.


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C.-S. Cheng. R. A. Bailey. "Optimality of Some Two-Associate-Class Partially Balanced Incomplete-Block Designs." Ann. Statist. 19 (3) 1667 - 1671, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0741.62071
MathSciNet: MR1126346
Digital Object Identifier: 10.1214/aos/1176348270

Primary: 62K05
Secondary: 05B05

Keywords: optimal design , partially balanced incomplete-block design , regular graph design , strongly regular graph design

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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