Let X be a random vector uniformly distributed on the unit cube and $f: [0, 1]^3 \to \mathsf{R}$ be a measurable function. An objective of many computer experiments is to estimate $\mu = E(f \circ X)$ by computing f at a set of points in $[0, 1]^3$. There is a design issue in choosing these points. Recently Owen and Tang independently suggested using randomized orthogonal arrays in the choice of such a set. This paper investigates the convergence rate to normality of the distribution of the average of a set of f values taken from one of these designs.
@article{1032526964,
author = {Loh, Wei-Liem},
title = {A combinatorial central limit theorem for randomized orthogonal array sampling designs},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 1209-1224},
language = {en},
url = {http://dml.mathdoc.fr/item/1032526964}
}
Loh, Wei-Liem. A combinatorial central limit theorem for randomized orthogonal array sampling designs. Ann. Statist., Tome 24 (1996) no. 6, pp. 1209-1224. http://gdmltest.u-ga.fr/item/1032526964/