Canadian Journal of Statistics

Approximate theory of multiway block designs

Journal Article

Abstract

Optimality properties of multiway block designs are deduced from the general results of J. Kiefer's approximate‐design theory. In the model with additive effects these optimality properties solely depend on the two‐dimensional marginals of the designs. Uniform designs, and designs whose two‐dimensional marginals are products of the one‐dimensional marginals, are shown to be optimal. Approximate Youden designs are introduced for the case when the support sets of the two‐dimensional marginals are prescribed in advance. They are optimal in a relatively small class of competing designs only.

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