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A new rotation method for constructing orthogonal Latin hypercube designs

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Abstract

Latin hypercube designs (LHDs) are very popular in designing computer experiments. In addition, orthogonality is a desirable property for LHDs, as it allows the estimates of the main effects in linear models to be uncorrelated with each other, and is a step** stone to the space-filling property for fitting Gaussian process models. Among the available methods for constructing orthogonal Latin hypercube designs (OLHDs), the rotation method is particularly attractive due to its theoretical elegance as well as its contribution to space-filling properties in low dimensional projections. This paper proposes a new rotation method for constructing OLHDs and nearly OLHDs with flexible run sizes that cannot be obtained by existing methods. Furthermore, the resulting OLHDs are improved in terms of the maximin distance criterion and the alias matrices and a new kind of orthogonal designs are constructed. Theoretical properties as well as construction algorithms are provided.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 12131001 and 11871288), National Ten Thousand Talents Program and the 111 Project B20016. The authors thank the referees for their helpful comments and suggestions. The first two authors contributed equally to this work.

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Authors and Affiliations

  1. National Key Laboratory for Complex Systems Simulation, Bei**g, 100101, China

    Chong Sheng

  2. School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tian**, 300071, China

    Chong Sheng, **yu Yang & Min-Qian Liu

Authors
  1. Chong Sheng
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  2. **yu Yang
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  3. Min-Qian Liu
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Correspondence to Min-Qian Liu.

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Sheng, C., Yang, J. & Liu, MQ. A new rotation method for constructing orthogonal Latin hypercube designs. Sci. China Math. 66, 839–854 (2023). https://doi.org/10.1007/s11425-020-1996-1

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  • DOI: https://doi.org/10.1007/s11425-020-1996-1

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