OPTIMALITY OF SOME 2-ASSOCIATE-CLASS PARTIALLY BALANCED INCOMPLETE-BLOCK DESIGNS
成果类型：
Article
署名作者：
CHENG, CS; BAILEY, RA
署名单位：
UK Research & Innovation (UKRI); Biotechnology and Biological Sciences Research Council (BBSRC); Rothamsted Research
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348270
发表日期：
1991
页码：
1667-1671
关键词：
摘要：
Let D(v, b, k) be the set of all the binary equireplicate incomplete-block designs for v treatments in b blocks of size k. It is shown that if D(v, b, k) contains a connected two-associate-class partially balanced design d* with lambda-2 = lambda-1 +/- 1 which has a singular concurrence matrix, then it is optimal over D(v, b, k) with respect to a large class of criteria including the A, D and E criteria. The dual of d* is also optimal over D(b, v, r) with respect to the same criteria, where r = bk/v. 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.