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].

Keywords:

• Combinatorial central limit theorem
• Computer experiment
• Orthogonal array
• Random permutation
• Stein's method

Mathematics Subject Classification:

• Primary 62E20
• Secondary 60F05, 62D05