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August 2008 A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments
Wei-Liem Loh
Ann. Statist. 36(4): 1983-2023 (August 2008). DOI: 10.1214/07-AOS530

Abstract

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].

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Wei-Liem Loh. "A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments." Ann. Statist. 36 (4) 1983 - 2023, August 2008. https://doi.org/10.1214/07-AOS530

Information

Published: August 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1143.62044
MathSciNet: MR2435462
Digital Object Identifier: 10.1214/07-AOS530

Subjects:
Primary: 62E20
Secondary: 60F05 , 65C05

Keywords: computer experiment , multivariate central limit theorem , numerical integration , OA-based Latin hypercube , randomized orthogonal array , Stein’s method

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 4 • August 2008
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