Construction of uniform mixed-level designs through level permutations

Bochuan Jiang (), Fei Wang () and Yaping Wang ()
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Bochuan Jiang: Beijing Jiaotong University
Fei Wang: Peking University
Yaping Wang: East China Normal University

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 6, No 5, 753-770

Abstract: Abstract Uniform designs have been widely used in physical and computer experiments due to their robust performances. The level permutation method can efficiently construct uniform designs with both lower discrepancy and less aberration. However, the related existing literature has mostly discussed uniform fixed-level designs, the construction of uniform mixed-level designs has been quite few studied. In this paper, a novel level permutation method for constructing uniform mixed-level designs is proposed. Our main idea is to perform level permutations on a new class of designs, called minimum average discrepancy designs, rather than generalized minimum aberration designs as in the fixed-level case. Several theoretical results on the design optimality and construction are obtained. Numerical results suggest the good performance of the resulting designs under various popular discrepancies.

Keywords: Average discrepancy; Level permutation; Lower bound; Mixed-level design; Uniform design; 62K15; 62K10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00850-1

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