A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments

Details A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments

2007-08-05

arxiv.org/abs/0708.0656v1

Mathematics

Statistics Theory

89 pages

Scientific paper

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 [Owen (1992a)] as well as for a class of OA-based Latin hypercubes [Tang (1993)].

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