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

TL;DR

This paper proves a multivariate central limit theorem for randomized orthogonal array sampling designs and OA-based Latin hypercubes, providing theoretical foundations for their use in computer experiments.

Contribution

It establishes a multivariate CLT for these sampling designs, advancing the theoretical understanding of their statistical properties.

Findings

Multivariate CLT holds for randomized orthogonal array sampling designs.

Results apply to OA-based Latin hypercubes.

Provides theoretical justification for these designs in computer experiments.

Abstract

Let $f:[0,1)^d \to {\mathbb R}$ 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 (1992a)] as well as for a class of OA-based Latin hypercubes [Tang (1993)].