The Annals of Statistics

Strong orthogonal arrays of strength two plus

Yuanzhen He, Ching-Shui Cheng, and Boxin Tang

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Strong orthogonal arrays were recently introduced and studied in He and Tang [Biometrika 100 (2013) 254–260] as a class of space-filling designs for computer experiments. To enjoy the benefits of better space-filling properties, when compared to ordinary orthogonal arrays, strong orthogonal arrays need to have strength three or higher, which may require run sizes that are too large for experimenters to afford. To address this problem, we introduce a new class of arrays, called strong orthogonal arrays of strength two plus. These arrays, while being more economical than strong orthogonal arrays of strength three, still enjoy the better two-dimensional space-filling property of the latter. Among the many results we have obtained on the characterizations and constructions of strong orthogonal arrays of strength two plus, worth special mention is their intimate connection with second-order saturated designs.

Article information

Ann. Statist., Volume 46, Number 2 (2018), 457-468.

Received: August 2016
Revised: February 2017
First available in Project Euclid: 3 April 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Complementary design computer experiment Latin hypercube second-order saturated design space-filling design


He, Yuanzhen; Cheng, Ching-Shui; Tang, Boxin. Strong orthogonal arrays of strength two plus. Ann. Statist. 46 (2018), no. 2, 457--468. doi:10.1214/17-AOS1555.

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