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

Abstract

Let f : [0, 1)^d→ℝ be an integrable function. An objective of many computer experiments is to estimate ∫_{[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].