Resolvable Designs with Large Blocks

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 concurrence...

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Bibliographic Details
Published in:The Annals of statistics 2007-04, Vol.35 (2), p.747-771
Main Authors: Morgan, J. P., Reck, Brian H.
Format: Article
Language:English
Subjects:
05B05
62K05
62K10
Adjacency matrix
Agriculture
balanced array
Combinatorics
Combinatorics. Ordered structures
Design efficiency
Designs and configurations
dual design
Eigenvalues
Exact sciences and technology
Experiment design
Experimental Design
Experimentation
General topics
Integers
Mathematical models
Mathematics
Matrices
Matrix
optimal design
Optimization
Probability and statistics
Real numbers
Resolvable block design
Sciences and techniques of general use
Statistical methods
Statistics
Studies
Sufficiency and information
Sufficient conditions
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Summary: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.
ISSN:0090-5364
2168-8966
DOI:10.1214/009053606000001253