The Annals of Statistics

A central limit theorem for general orthogonal array based space-filling designs

Xu He and Peter Z. G. Qian

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 42, Number 5 (2014), 1725-1750.

Dates
First available in Project Euclid: 11 September 2014

Permanent link to this document
https://projecteuclid.org/euclid.aos/1410440623

Digital Object Identifier
doi:10.1214/14-AOS1231

Mathematical Reviews number (MathSciNet)
MR3262466

Zentralblatt MATH identifier
1301.30040

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E20: Asymptotic distribution theory 62K99: None of the above, but in this section 05B15: Orthogonal arrays, Latin squares, Room squares

Keywords
Computer experiment design of experiment method of moment numerical integration uncertainty quantification

Citation

He, Xu; Qian, Peter Z. G. A central limit theorem for general orthogonal array based space-filling designs. Ann. Statist. 42 (2014), no. 5, 1725--1750. doi:10.1214/14-AOS1231. https://projecteuclid.org/euclid.aos/1410440623


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