The Annals of Statistics
- Ann. Statist.
- Volume 6, Number 6 (1978), 1239-1261.
Optimality of Certain Asymmetrical Experimental Designs
The problem of finding an optimal design for the elimination of one-way heterogeneity when a balanced block design does not exist is studied. A general result on the optimality of certain asymmetrical designs is proved and applied to the block design setting. It follows that if there is a group divisible partially balanced block design (GD PBBD) with 2 groups and $\lambda_2 = \lambda_1 + 1$, then it is optimal w.r.t. a very general class of criteria including all the commonly used ones. On the other hand, if there is a GD PBBD with 2 groups and $\lambda_1 = \lambda_2 + 1$, then it is optimal w.r.t. another class of criteria. Uniqueness of optimal designs and some other miscellaneous results are also obtained.
Ann. Statist. Volume 6, Number 6 (1978), 1239-1261.
First available in Project Euclid: 12 April 2007
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Cheng, Ching-Shui. Optimality of Certain Asymmetrical Experimental Designs. Ann. Statist. 6 (1978), no. 6, 1239--1261. doi:10.1214/aos/1176344371. http://projecteuclid.org/euclid.aos/1176344371.