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A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments
Wei-Liem Loh
Source: Ann. Statist. Volume 36, Number 4 (2008), 1983-2023.
Abstract
Let f : [0, 1)d→ℝ be an integrable function. An objective of many computer experiments is to estimate ∫[0, 1)d f(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].
Primary Subjects: 62E20
Secondary Subjects: 60F05, 65C05
Keywords: Computer experiment; multivariate central limit theorem; numerical integration; OA-based Latin hypercube; randomized orthogonal array; Stein’s method
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1216237306
Digital Object Identifier: doi:10.1214/07-AOS530
Mathematical Reviews number (MathSciNet):
MR2435462
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