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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


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.


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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.


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

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

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


Vol.42 • No. 5 • October 2014
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