## The Annals of Statistics

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

#### 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

https://projecteuclid.org/euclid.aos/1410440623

Digital Object Identifier
doi:10.1214/14-AOS1231

Mathematical Reviews number (MathSciNet)
MR3262466

Zentralblatt MATH identifier
1301.30040

#### 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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