## Annals of Statistics

### A characterization of strong orthogonal arrays of strength three

#### Abstract

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

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

Dates
First available in Project Euclid: 25 June 2014

https://projecteuclid.org/euclid.aos/1403715203

Digital Object Identifier
doi:10.1214/14-AOS1225

Mathematical Reviews number (MathSciNet)
MR3226159

Zentralblatt MATH identifier
1306.62188

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1403715203

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