A stratified L 2 -discrepancy with application to space-filling designs
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2026 · Volume 88 · Issue 2
Abstract
Space-filling designs are widely used in computer experiments. We propose a stratifiedL2-discrepancy to evaluate the uniformity of a design when the design domain is stratified into various subregions. Weights are used to adjust preferences for the uniformity over subregions in each stratification. The stratifiedL2-discrepancy is easy to compute, satisfies a Koksma–Hlawka type inequality, and overcomes the curse of dimensionality that exists for other discrepancies. It is applicable to a broad class of designs, and covers several minimum aberration-type criteria as special cases. Strong orthogonal arrays of maximum strength are shown to have low stratifiedL2-discrepancies, and thus are suitable for computer experiments. In addition, we develop a lower bound for the stratifiedL2-discrepancy and provide a construction method for designs that achieve the lower bound. We further introduce a general version of the stratifiedL2-discrepancy for evaluating designs with flexible stratification properties.
Keywords
computer experiment, curse of dimensionality, generalised minimum aberration, space-filling hierarchy principle, strong orthogonal array
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