A combinatorial central limit theorem for randomized orthogonal array sampling designs

Abstract

Let X be a random vector uniformly distributed on the unit cube and $f: [0, 1]^3 \to \mathsf{R}$ be a measurable function. An objective of many computer experiments is to estimate $\mu = E(f \circ X)$ by computing f at a set of points in $[0, 1]^3$. There is a design issue in choosing these points. Recently Owen and Tang independently suggested using randomized orthogonal arrays in the choice of such a set. This paper investigates the convergence rate to normality of the distribution of the average of a set of f values taken from one of these designs.