A Non-uniform Concentration Inequality for Randomized Orthogonal Array Sampling Designs

K. Laipaporn, K. Neammanee

Abstract

Let $ f : [0; 1]^3 \rightarrow R$ be a measurable function. In many computer experiments, we estimate the value of $\int _{[0,1]^3}f (x) dx$ , which is the mean $\mu = E (f \circ X), where X is a uniform random vector on the unit hypercube $[0; 1]^3$. In 1992 and 1993, Owen and Tang introduced randomized orthogonal arrays to choose the sampling points to estimate the integral.

In this paper, we give a non-uniform concentration inequality for randomized

orthogonal array

sampling designs.