The Annals of Statistics

Resolvable designs with large blocks

J. P. Morgan and Brian H. Reck

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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.

Article information

Ann. Statist., Volume 35, Number 2 (2007), 747-771.

First available in Project Euclid: 5 July 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs
Secondary: 62K10: Block designs 05B05: Block designs [See also 51E05, 62K10]

Resolvable block design optimal design dual design balanced array


Morgan, J. P.; Reck, Brian H. Resolvable designs with large blocks. Ann. Statist. 35 (2007), no. 2, 747--771. doi:10.1214/009053606000001253.

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