Resolvable designs with large blocks

Details Resolvable designs with large blocks Resolvable designs with large blocks

2007-08-14

arxiv.org/abs/0708.1896v1

Annals of Statistics 2007, Vol. 35, No. 2, 747-771

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001253 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001253

Resolvable designs with two blocks per replicate are studied from an optimality perspective. Because in practice the number of replicates is typically less than the number of treatments, arguments can be based on the dual of the information matrix and consequently given in terms of block concurrences. Equalizing block concurrences for given block sizes is often, but not always, the best strategy. Sufficient conditions are established for various strong optimalities and a detailed study of E-optimality is offered, including a characterization of the E-optimal class. Optimal designs are found to correspond to balanced arrays and an affine-like generalization.

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