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.
Publié le : 1978-11-14
Classification:
Block designs,
type 1 criteria,
type 2 criteria,
regular graph designs,
(M.S)-optimality,
most-balanced group divisible partially balanced block designs,
62K05,
62K10
@article{1176344371,
author = {Cheng, Ching-Shui},
title = {Optimality of Certain Asymmetrical Experimental Designs},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 1239-1261},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344371}
}
Cheng, Ching-Shui. Optimality of Certain Asymmetrical Experimental Designs. Ann. Statist., Tome 6 (1978) no. 1, pp. 1239-1261. http://gdmltest.u-ga.fr/item/1176344371/