Connections Among Different Criteria for Optimal Factor Assignments

Abstract

The objective of this article is to study the connections of different criteria, which come from different statistical models, for optimal factor assignments. The asymptotic Bayes criterion is firstly developed in terms of the asymptotic approach of Mitchell et al. (1994) for a more general covariance kernel than the one which used in Yue and Chatterjee (2010). A relationship between the asymptotic Bayes criterion and other criteria, such as orthogonality and aberration, is built. A lower bound for the criterion is also obtained, and numerical results show that this lower bound is tight. Our results generalize those in Yue and Chatterjee (2010) from symmetrical case to asymmetrical U-type design.

Keywords:

• Asymmetrical U-type design
• Bayesian design
• Generalized minimum aberration
• Orthogonality

Mathematics Subject Classification:

• 62K05
• 62J02

Acknowledgments

The authors would like to thank the Referees and Chief Editor for their valuable comments and suggestions that lead to improve the presentation of the article. This work was partially supported by SRFDP (No. 20090144110002), the National Natural Science Foundation of China (Grant No. 10671080), NCET (No. 06-672), Scientific Research Plan Item of Hunan Provincial Department of Education (No. 10C1091), the Innovation Program and Independent Research Project Funded by Central China Normal University.