The Annals of Statistics

A characterization of strong orthogonal arrays of strength three

Yuanzhen He and Boxin Tang

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In an early paper, He and Tang [Biometrika 100 (2013) 254–260] introduced and studied a new class of designs, strong orthogonal arrays, for computer experiments, and characterized such arrays through generalized orthogonal arrays. The current paper presents a simple characterization for strong orthogonal arrays of strength three. Besides being simple, this new characterization through a notion of semi-embeddability is more direct and penetrating in terms of revealing the structure of strong orthogonal arrays. Some other results on strong orthogonal arrays of strength three are also obtained along the way, and in particular, two $\operatorname{SOA}(54,5,27,3)$’s are constructed.

Article information

Ann. Statist., Volume 42, Number 4 (2014), 1347-1360.

First available in Project Euclid: 25 June 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K15: Factorial designs
Secondary: 05B15: Orthogonal arrays, Latin squares, Room squares

Computer experiment low dimensional projection Latin hypercube space-filling design $(t,m,s)$-net


He, Yuanzhen; Tang, Boxin. A characterization of strong orthogonal arrays of strength three. Ann. Statist. 42 (2014), no. 4, 1347--1360. doi:10.1214/14-AOS1225.

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