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Let $f:[0,1)^d \to {\mathbb R}$ be an integrable function. An objective ofmany computer experiments is to estimate $\int_{[0,1)^d} f(x) dx$ by evaluatingf at a finite number of points in [0,1)^d. There is a design issue in thechoice of these points and a popular choice is via the use of randomizedorthogonal arrays. This article proves a multivariate central limit theorem fora class of randomized orthogonal array sampling designs [Owen (1992a)] as wellas for a class of OA-based Latin hypercubes [Tang (1993)].

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