Design efficiency for minimum projection uniform designs with q levels

Qiming Bai, Hongyi Li (), Xingyou Huang and Huili Xue
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Qiming Bai: Jishou University
Hongyi Li: Jishou University
Xingyou Huang: Jishou University
Huili Xue: Jishou University

Metrika: International Journal for Theoretical and Applied Statistics, 2023, vol. 86, issue 5, No 4, 577-594

Abstract: Abstract Minimum projection uniform designs and high efficient designs are two kinds of excellent designs in design of experiment. In this paper, design efficiency for minimum projection uniform designs with q levels is discussed. Firstly, the uniformity pattern of q-level designs is proposed based on the centered $$L_2$$ L 2 -discrepancy. Secondly, the analytical connection between uniformity pattern and design efficiency is established for the q-level orthogonal arrays with strength 2, and for the orthogonal arrays with strength 3, the minimum projection uniformity criterion is equivalent to the design efficiency criterion. Finally, a tight lower bound of uniformity pattern is presented, which is used as a benchmark for measuring the uniformity of projection designs.

Keywords: Minimum projection uniform design; Design efficiency; Orthogonal array; Centered $$L_2$$ L 2 -discrepancy; Lower bound; 62K15; 62K05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00184-022-00885-y

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