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

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.