## The Annals of Statistics

### Construction of E(s2)-optimal supersaturated designs

#### Abstract

Booth and Cox proposed the E(s2) 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(s2). 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(s2)-optimal designs are obtained by using a computer to search for designs that achieve the improved bounds.

#### Article information

Source
Ann. Statist. Volume 32, Number 4 (2004), 1662-1678.

Dates
First available in Project Euclid: 4 August 2004

Permanent link to this document
http://projecteuclid.org/euclid.aos/1091626182

Digital Object Identifier
doi:10.1214/009053604000000472

Mathematical Reviews number (MathSciNet)
MR2089137

Zentralblatt MATH identifier
1105.62362

Subjects
Primary: 62K15: Factorial designs
Secondary: 62K10: Block designs

#### Citation

Bulutoglu, Dursun A.; Cheng, Ching-Shui. Construction of E ( s 2 )-optimal supersaturated designs. Ann. Statist. 32 (2004), no. 4, 1662--1678. doi:10.1214/009053604000000472. http://projecteuclid.org/euclid.aos/1091626182.

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