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Theory and applications of stratification criteria based on space-filling pattern and projection pattern

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Abstract

Space-filling designs are crucial for computer experiments. The quality of a space-filling design can be appropriately reflected by its stratification properties. In a recent paper, Tian and Xu (Biometrika 109(2):489–501, 2022) introduced the concept of a space-filling pattern to properly characterize a design’s stratification properties on various grids. In this study, we generalize the space-filling pattern using arbitrary orthonormal contrasts. We also propose a new pattern called the two-dimensional projection pattern to capture the stratification properties of balanced designs in two dimensions more comprehensively. We derive some theoretical results for both patterns and show that they are easier to compute and apply to a wider range of designs. We further show the use of the two patterns in constructing space-filling designs based on existing strong orthogonal arrays.

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Acknowledgements

We are grateful to the referee editor and two reviewers for their insightful comments and constructive suggestions. This study was supported by the National Natural Science Foundation of China (Grant Nos. 12371259, 11971098, 12271166, 11901199 and 12061033) and the National Key Research and Development Program of China (Nos. 2020YFA0714102 and 2022YFA1003701).

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  1. ** Wang have contributed equally to this work.

Authors and Affiliations

  1. KLAS and School of Mathematics and Statistics, Northeast Normal University, No.5268, Renmin Street, Changchun, 130024, China

    ** Wang

  2. Department of Science and Technology, Hulunbuir University, No.26, Middle Genghis Khan Road, Hailar District, Hulunbuir, 021008, China

    **nqi Zhang

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  1. **nqi Zhang
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  2. Fasheng Sun
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Correspondence to Fasheng Sun.

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Zhang, X., Wang, Y. & Sun, F. Theory and applications of stratification criteria based on space-filling pattern and projection pattern. Metrika (2024). https://doi.org/10.1007/s00184-024-00964-2

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