Open Access
Translator Disclaimer
October 2014 A central limit theorem for general orthogonal array based space-filling designs
Xu He, Peter Z. G. Qian
Ann. Statist. 42(5): 1725-1750 (October 2014). DOI: 10.1214/14-AOS1231

Abstract

Orthogonal array based space-filling designs (Owen [Statist. Sinica 2 (1992a) 439–452]; Tang [J. Amer. Statist. Assoc. 88 (1993) 1392–1397]) have become popular in computer experiments, numerical integration, stochastic optimization and uncertainty quantification. As improvements of ordinary Latin hypercube designs, these designs achieve stratification in multi-dimensions. If the underlying orthogonal array has strength $t$, such designs achieve uniformity up to $t$ dimensions. Existing central limit theorems are limited to these designs with only two-dimensional stratification based on strength two orthogonal arrays. We develop a new central limit theorem for these designs that possess stratification in arbitrary multi-dimensions associated with orthogonal arrays of general strength. This result is useful for building confidence statements for such designs in various statistical applications.

Citation

Download Citation

Xu He. Peter Z. G. Qian. "A central limit theorem for general orthogonal array based space-filling designs." Ann. Statist. 42 (5) 1725 - 1750, October 2014. https://doi.org/10.1214/14-AOS1231

Information

Published: October 2014
First available in Project Euclid: 11 September 2014

zbMATH: 1301.30040
MathSciNet: MR3262466
Digital Object Identifier: 10.1214/14-AOS1231

Subjects:
Primary: 60F05
Secondary: 05B15 , 62E20 , 62K99

Keywords: computer experiment , design of experiment , method of moment , numerical integration , uncertainty quantification

Rights: Copyright © 2014 Institute of Mathematical Statistics

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.42 • No. 5 • October 2014
Back to Top