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A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments. (English) Zbl 1143.62044

Summary: Let \(f:[0,1)^d\to\mathbb R\) be an integrable function. An objective of many computer experiments is to estimate \(\int_{[0, 1)^d} f(x)\,dx\) by evaluating \(f\) at a finite number of points in \([0,1)^d\). There is a design issue in the choice of these points and a popular choice is via the use of randomized orthogonal arrays. This article proves a multivariate central limit theorem for a class of randomized orthogonal array sampling designs [A. B. Owen, Stat. Sin. 2, No. 2, 439–452 (1992; Zbl 0822.62064); Corrigendumm ibid. 3, No. 1, 260 (1992)] as well as for a class of OA-based Latin hypercubes [B. Tang, J. Am. Stat. Assoc. 88, No. 424, 1392–1397 (1993; Zbl 0792.62066)].

MSC:

62K99 Design of statistical experiments
60F05 Central limit and other weak theorems
65C60 Computational problems in statistics (MSC2010)
05B15 Orthogonal arrays, Latin squares, Room squares
62E20 Asymptotic distribution theory in statistics
65D30 Numerical integration
62J10 Analysis of variance and covariance (ANOVA)
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References:

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