A Multivariate Central Limit Theorem for Randomized Orthogonal Array Sampling Designs in Computer Experiments

Let $f\colon [0,1)^{d}\rightarrow {\Bbb R}$ 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 Statist. Sinica 2 (1992a) 439-452] as well as for a class of OA-based Latin hypercubes [Tang J. Amer. Statist. Assoc. 81 (1993) 1392-1397].