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November, 1978 Optimal Designs for the Elimination of Multi-Way Heterogeneity
Ching-Shui Cheng
Ann. Statist. 6(6): 1262-1272 (November, 1978). DOI: 10.1214/aos/1176344372


The purpose of this paper is to study optimal designs for the elimination of multi-way heterogeneity. The $C$-matrix for the $n$-way heterogeneity setting when $n > 2$ is derived. It turns out to be a natural extension of the known formulas in the lower dimensional case. It is shown that under some regularity, the search for optimal designs can be reduced to that in a lower-way setting. Youden hyperrectangles are defined as higher dimensional generalizations of balanced block designs and generalized Youden designs. When all the sides are equal, they are called Youden hypercubes. It is shown that a Youden hyperrectangle is $E$-optimal and a Youden hypercube is $A$- and $D$-optimal. The latter is quite interesting since it is not always true in two-way settings.


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Ching-Shui Cheng. "Optimal Designs for the Elimination of Multi-Way Heterogeneity." Ann. Statist. 6 (6) 1262 - 1272, November, 1978.


Published: November, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0401.62060
MathSciNet: MR523761
Digital Object Identifier: 10.1214/aos/1176344372

Primary: 62K05
Secondary: 62K10

Keywords: $A$-optimality , $C$-matrix , $D$-optimality , $E$-optimality , regular settings , universal optimality , Youden hypercube , Youden hyperrectangle

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 6 • November, 1978
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