The Annals of Statistics
- Ann. Statist.
- Volume 42, Number 5 (2014), 1725-1750.
A central limit theorem for general orthogonal array based space-filling designs
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.
Ann. Statist., Volume 42, Number 5 (2014), 1725-1750.
First available in Project Euclid: 11 September 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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