A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments
Open Access
- 1 August 2008
- journal article
- research article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 36 (4), 1983-2023
- https://doi.org/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)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].Keywords
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