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Biometrika Advance Access originally published online on May 15, 2007
Biometrika 2007 94(2):459-468; doi:10.1093/biomet/asm039
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Copyright © 2007 Biometrika Trust

Articles

Optimal nested row-column designs with specified components

R. A. Bailey

School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, U.K.

E. R. Williams

Statistical Consulting Unit, The Australian National University, Canberra ACT 0200, Australia

r.a.bailey{at}qmul.ac.uk

emlyn.williams{at}anu.edu.au

Received for publication 1 April 2006. Revision received 1 October 2006.
  Abstract

We consider nested row-column designs where each of the row and column component designs is specified. For the case that each of the component designs has second-order balance, we define such a nested row-column design to be special if it is generally balanced, with the smallest possible number of canonical treatment contrasts having the lower canonical efficiency factor in both components. We show that if any special row-column design exists then it is A-optimal over all nested row-column designs with the given components.

Key Words: Canonical efficiency factor • General balance • Lattice square • Second-order balance • Special row-column design


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