Orthogonal array-based Latin hypercubes. (English) Zbl 0792.62066

Tang, Boxin

J. Am. Stat. Assoc. 88, No. 424, 1392-1397 (1993).

Summary: We use orthogonal arrays (OA’s) to construct Latin hypercubes. Besides preserving the univariate stratification properties of Latin hypercubes, these strength \(r\) OA-based Latin hypercubes also stratify each \(r\)- dimensional margin. Therefore, such OA-based Latin hypercubes provide more suitable designs for computer experiments and numerical integration than do general Latin hypercubes. We prove that when used for integration, the sampling scheme with OA-based Latin hypercubes offers a substantial improvement over Latin hypercube sampling.

MSC:

62K99	Design of statistical experiments
65C99	Probabilistic methods, stochastic differential equations

Keywords:

orthogonal arrays; Latin hypercubes; stratification properties; computer experiments; numerical integration