Construction of E(s^2)-optimal supersaturated designs

Details Construction of E(s^2)-optimal supersaturated designs Construction of E(s^2)-optimal supersaturated designs

2004-10-05

arxiv.org/abs/math/0410090v1

Annals of Statistics 2004, Vol. 32, No. 4, 1662-1678

Mathematics

Statistics Theory

Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat

Scientific paper

10.1214/009053604000000472

Booth and Cox proposed the E(s^2) criterion for constructing two-level supersaturated designs. Nguyen [Technometrics 38 (1996) 69-73] and Tang and Wu [Canad. J. Statist 25 (1997) 191-201] independently derived a lower bound for E(s^2). This lower bound can be achieved only when m is a multiple of N-1, where m is the number of factors and N is the run size. We present a method that uses difference families to construct designs that satisfy this lower bound. We also derive better lower bounds for the case where the Nguyen-Tang-Wu bound is not achievable. Our bounds cover more cases than a bound recently obtained by Butler, Mead, Eskridge and Gilmour [J. R. Stat. Soc. Ser. B Stat. Methodol. 63 (2001) 621-632]. New E(s^2)-optimal designs are obtained by using a computer to search for designs that achieve the improved bounds.

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