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Nested orthogonal array-based Latin hypercube designs

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  • Xu He
  • Peter Z. G. Qian

Abstract

We propose two methods for constructing a new type of design, called a nested orthogonal array-based Latin hypercube design, intended for multi-fidelity computer experiments. Such designs are two nested space-filling designs in which the large design achieves stratification in both bivariate and univariate margins and the small design achieves stratification in univariate margins. These designs have better space-filling properties than nested Latin hypercube designs in which the large design possesses uniformity in univariate margins only. The first method expands an ordinary Latin hypercube design to a larger design that achieves uniformity in any one- or two-dimensional projection. The second method uses an orthogonal array with strength two to simultaneously construct a pair of nested orthogonal array-based Latin hypercube designs. Examples are given to illustrate the proposed methods. Sampling properties of the proposed designs are derived. Copyright 2011, Oxford University Press.

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  • Xu He & Peter Z. G. Qian, 2011. "Nested orthogonal array-based Latin hypercube designs," Biometrika, Biometrika Trust, vol. 98(3), pages 721-731.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:3:p:721-731
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    File URL: http://hdl.handle.net/10.1093/biomet/asr028
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    Cited by:

    1. Jin Xu & Jiajie Chen & Peter Z. G. Qian, 2015. "Sequentially Refined Latin Hypercube Designs: Reusing Every Point," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1696-1706, December.
    2. Xu, Jin & Duan, Xiaojun & Wang, Zhengming & Yan, Liang, 2018. "A general construction for nested Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 134-140.

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