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

TL;DR

This paper establishes a new central limit theorem for orthogonal array based space-filling designs with multi-dimensional stratification, enhancing statistical inference in complex experimental settings.

Contribution

It extends existing CLTs to designs with arbitrary multi-dimensional stratification from orthogonal arrays of any strength, broadening their theoretical foundation.

Findings

Proves a CLT for general orthogonal array based designs

Enables confidence interval construction for complex designs

Supports advanced statistical applications in experiments

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.