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

摘要

Let f : [0, 1)(d) -> R be an integrable function. An objective of many computer experiments is to estimate integral(d)([0, 1)) 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.