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Construction of Uniform Designs on Arbitrary Domains by Inverse Rosenblatt Transformation

In: Contemporary Experimental Design, Multivariate Analysis and Data Mining

Author

Listed:
  • Mei Zhang

    (Sichuan University, College of Mathematics)

  • Aijun Zhang

    (The University of Hong Kong, Department of Statistics and Actuarial Science)

  • Yongdao Zhou

    (Nankai University, School of Statistics and Data Science & LPMC)

Abstract

The uniform design proposed by Fang [6] and Wang and Fang [17] has become an important class of designs for both traditional industrial experiments and modern computer experiments. There exist established theory and methods for constructing uniform designs on hypercube domains, while the uniform design construction on arbitrary domains remains a challenging problem. In this paper, we propose a deterministic construction method through inverse Rosenblatt transformation, as a general approach to convert the uniformly designed points from the unit hypercubes to arbitrary domains. To evaluate the constructed designs, we employ the central composite discrepancy as a uniformity measure suitable for irregular domains. The proposed method is demonstrated with a class of flexible regions, constrained and manifold domains, and the geographical domain with very irregular boundary. The new construction results are shown competitive to traditional stochastic representation and acceptance-rejection methods.

Suggested Citation

  • Mei Zhang & Aijun Zhang & Yongdao Zhou, 2020. "Construction of Uniform Designs on Arbitrary Domains by Inverse Rosenblatt Transformation," Springer Books, in: Jianqing Fan & Jianxin Pan (ed.), Contemporary Experimental Design, Multivariate Analysis and Data Mining, chapter 0, pages 111-126, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-46161-4_7
    DOI: 10.1007/978-3-030-46161-4_7
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