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].
Publié le : 2008-08-15
Classification:
Computer experiment,
multivariate central limit theorem,
numerical integration,
OA-based Latin hypercube,
randomized orthogonal array,
Stein’s method,
62E20,
60F05,
65C05
@article{1216237306,
author = {Loh, Wei-Liem},
title = {A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments},
journal = {Ann. Statist.},
volume = {36},
number = {1},
year = {2008},
pages = { 1983-2023},
language = {en},
url = {http://dml.mathdoc.fr/item/1216237306}
}
Loh, Wei-Liem. A multivariate central limit theorem for randomized orthogonal array sampling designs in computer experiments. Ann. Statist., Tome 36 (2008) no. 1, pp. 1983-2023. http://gdmltest.u-ga.fr/item/1216237306/