The Annals of Statistics

A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments

Wei-Liem Loh

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Let f : [0, 1)d→ℝ be an integrable function. An objective of many computer experiments is to estimate [0, 1)df(x) dx by evaluating f at a finite number of points in [0, 1)d. There is a design issue in the choice of these points and a popular choice is via the use of randomized orthogonal arrays. This article proves a multivariate central limit theorem for a class of randomized orthogonal array sampling designs [Owen Statist. Sinica 2 (1992a) 439–452] as well as for a class of OA-based Latin hypercubes [Tang J. Amer. Statist. Assoc. 81 (1993) 1392–1397].

Article information

Ann. Statist., Volume 36, Number 4 (2008), 1983-2023.

First available in Project Euclid: 16 July 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62E20: Asymptotic distribution theory
Secondary: 60F05: Central limit and other weak theorems 65C05: Monte Carlo methods

Computer experiment multivariate central limit theorem numerical integration OA-based Latin hypercube randomized orthogonal array Stein’s method


Loh, Wei-Liem. A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments. Ann. Statist. 36 (2008), no. 4, 1983--2023. doi:10.1214/07-AOS530.

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