The Annals of Statistics

Resolvable designs with large blocks

J. P. Morgan and Brian H. Reck

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 5 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1183667292

Digital Object Identifier
doi:10.1214/009053606000001253

Mathematical Reviews number (MathSciNet)
MR2336867

Zentralblatt MATH identifier
1117.62075

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

Keywords
Resolvable block design optimal design dual design balanced array

Citation

Morgan, J. P.; Reck, Brian H. Resolvable designs with large blocks. Ann. Statist. 35 (2007), no. 2, 747--771. doi:10.1214/009053606000001253. https://projecteuclid.org/euclid.aos/1183667292


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