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A new class of Latin hypercube for computer experiments. (English) Zbl 1266.62049

Fan, Jianqing (ed.) et al., Contemporary multivariate analysis and design of experiments. In celebration of Professor Kai-Tai Fang’s 65th birthday. Most of the papers are presented at the international conference on statistics, Hong Kong, China, June 20–24, 2005. Hackensack, NJ: World Scientific (ISBN 981-256-120-X/hbk; 978-981-256-776-5/ebook). Series in Biostatistics 2, 205-226 (2005).
Summary: Computer models can describe complicated physical phenomena. To use these models for scientific investigations, however, their generally long running times and mostly deterministic nature require specially designed experiments. Standard factorial designs are inadequate; in the absence of one or more main effects, their replication cannot be used to estimate the errors but instead produce redundancy. A number of alternative designs have been proposed, but many can be burdensome computationally. This paper presents a class of Latin hypercube designs developed from the rotation of factorial designs. These rotated factorial designs are easy to construct and preserve many of the attractive properties of standard factorial designs: they have equally-spaced projections to univariate dimensions and yield uncorrelated regression effect estimates (orthogonality). They also rate comparably to maximin Latin hypercube designs by the minimum interpoint distance criterion used in the latter construction.
For the entire collection see [Zbl 1078.62524].

MSC:

62K10 Statistical block designs
05B15 Orthogonal arrays, Latin squares, Room squares
62K15 Factorial statistical designs
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