A Uniform Bound on a Combinatorial Central Limit Theorem for Randomized Orthogonal Array Sampling Designs

Abstract

Let X be a uniform random vector on the unit cube [0, 1]3 and f : [0, 1]3 → ℝ be a measurable function. In many computer experiments, we would like to estimate the value of ∈ t [0,1]3 f(x)dx, which is E(f○X), by computing f at a number points in [0, 1]3. There are many ways to choose these points and one of these is randomized orthogonal arrays which was proposed independently by Owen and Tang [10, 18], respectively. In this article, we give a uniform bound on a combinational central limit theorem for the randomized orthogonal arrays sampling designs which are based on OA(q 2, 3, q, 2) by using Stein's method. Our order is which is better than Loh's order [6].