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Theory and application of absolute discrepancy in experimental designs

Author

Listed:
  • Yao Xiao

    (Beijing Institute of Technology)

  • Hong Qin

    (Zhongnan University of Economics and Law)

  • Kashinath Chatterjee

    (Visva-Bharati University
    Population Health Sciences Medical College of Georgia at the Augusta University)

  • Na Zou

    (Zhongnan University of Economics and Law)

Abstract

In many practical experiments, the number of possible levels for each experimental factor is often limited to a finite number. Various discrepancies, like discrete discrepancy and Lee discrepancy, have been proposed to measure the uniformity on the discrete experimental domain. However, these two discrepancies can yield unreasonable results when multiple levels are involved. In this paper, a new discrepancy, termed absolute discrepancy (AD), is proposed as a more reasonable measure of uniformity on a discrete experimental domain, particularly for discrete-numerical factors. Moreover, connections between AD and other design optimality criteria, such as generalized minimum aberration and orthogonality, are established. These connections provide strong statistical justification for AD. Some lower bounds of AD are also obtained, serving as important benchmarks for the design uniformity. In addition, uniform designs based on the AD criterion have produced better prediction performance by fitting statistical surrogate models of complex surfaces compared to their competitors. Furthermore, the application in hyperparameter optimization for machine learning algorithms also validates the superiority of uniform designs with the proposed AD criterion.

Suggested Citation

  • Yao Xiao & Hong Qin & Kashinath Chatterjee & Na Zou, 2024. "Theory and application of absolute discrepancy in experimental designs," Statistical Papers, Springer, vol. 65(9), pages 5775-5795, December.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:9:d:10.1007_s00362-024-01617-2
    DOI: 10.1007/s00362-024-01617-2
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    References listed on IDEAS

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    1. Fasheng Sun & Jie Chen & Min-Qian Liu, 2011. "Connections between uniformity and aberration in general multi-level factorials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(3), pages 305-315, May.
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