Abstract
The objective of this paper is to discuss the issue of the projection uniformity of factorial designs measured by mixture discrepancy. The average projection discrepancy of combinatorially isomorphic designs obtained by level permutation on each factor is defined, which measures the projection uniformity on different dimensions. The uniformity pattern and minimum projection uniformity criterion for selecting optimal design are defined for q-level designs. The relationships between uniformity pattern, orthogonality and generalized word-length pattern are built. Moreover, a tight lower bound of uniformity pattern is also obtained.
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Acknowledgements
The authors greatly appreciate helpful suggestions of Editor-in-Chief and the referees. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11961027, 11561025, 11701213), Scientific Research Plan Item of Hunan Provincial Department of Education (Grant Nos. 19A403, 18A284).
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Wang, K., Ou, Z., Liu, J. et al. Uniformity pattern of q-level factorials under mixture discrepancy. Stat Papers 62, 1777–1793 (2021). https://doi.org/10.1007/s00362-019-01155-2
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DOI: https://doi.org/10.1007/s00362-019-01155-2
Keywords
- Average projection discrepancy
- Generalized minimum aberration
- Lower bound
- Mixture discrepancy
- Orthogonality