Abstract
The objective of this paper is to study the issue of the generalized projection discrepancy along the line of Qin et al. (J Stat Plan Inference 142:1170–1177, 2012) based on generalized discrete discrepancy measure proposed by Chatterjee and Qin (J Stat Plan Inference 141:951–960, 2011). We shall study the projection properties for general asymmetric factorials and provide some analytic connections between minimum generalized projection uniformity and other optimality criteria. A new lower bound on the generalized projection discrepancy for asymmetric factorials is presented here.
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References
Chatterjee K, Qin H (2011) Generalized discrete discrepancy and its applications in experimental designs. J Stat Plan Inference 141:951–960
Cheng CS, Deng LY, Tang B (2002) Generalized minimum aberration and design efficiency for nonregular fractional factorial designs. Stat Sin 12:991–1000
Fang KT, Ge GN, Liu MQ (2002) Uniform supersaturated design and its construction. Sci China Ser A 45(8):1080–1088
Fang KT, Lin DKJ, Liu MQ (2003) Optimal mixed-level supersaturated design. Metrika 58(3):279–291
Fang KT, Mukerjee R (2000) A connection between uniformity and aberration in regular fractions of two-level factorial. Biometrika 87(1):193–198
Fang KT, Qin H (2005) Uniformity pattern and related criteria for two-level factorials. Sci China Ser A 48:1–11
Hickernell FJ, Liu MQ (2002) Uniform designs limit aliasing. Biometrika 89:893–904
Liu MQ (2002) Using discrepancy to evaluate fractional factorial designs. In: Fang KT, Hickernell FJ, Niederreiter H (eds) Monte Carlo and Quasi-Monte Carlo methods 2000. Springer, Berlin, pp 357–368
Liu MQ, Fang KT, Hickernell FJ (2006) Connections among different criteria for asymmetrical fractional factorial designs. Stat Sin 16:1285–1297
Liu MQ, Hickernell FJ (2002) \(E(s^2)\)-optimality and minimum discrepancy in 2-level supersaturated designs. Stat Sin 12:931–939
Ma CX, Fang KT, Lin DKJ (2003) A note on uniformity and orthogonality. J Stat Plan Inference 113:323–334
Ou ZJ, Qin H (2010) Some applications of indicator function in two-level factorial designs. Stat Probab Lett 80:19–25
Qin H, Chatterjee K (2009) Lower bounds for the uniformity pattern of asymmetric fractional factorials. Commun Stat Theory Methods 38:1383–1392
Qin H, Fang KT (2004) Discrete discrepancy in factorial designs. Metrika 60:59–72
Qin H, Wang Z, Chatterjee K (2012) Uniformity pattern and related criteria for \(q\)-level factorials. J Stat Plan Inference 142:1170–1177
Qin H, Zou N, Zhang SL (2012) Design efficiency for minimum projection uniform designs with two-level. J Syst Sci Complic 24:761–768
Song S, Qin H (2010) Application of minimum projection uniformity criterion in complementary designs. Acta Math Sci 30:180–186
Xu H, Wu CFJ (2001) Generalized minimum aberration for asymmetrical fractional factorial designs. Ann Stat 29:549–560
Zhang AJ, Fang KT, Li R, Sudjianto A (2005) Majorization framework for balanced lattice designs. Ann Stat 33:2837–2853
Zhang SL, Qin H (2006) Minimum projection uniformity criterion and its application. Stat Probab Lett 76:634–640
Acknowledgments
The authors greatly appreciate helpful suggestions of the referees and the editor that greatly improved the paper. This research was partially supported by the NNSF of China (No. 11271147).
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Balakrishnan, N., Qin, H. & Chatterjee, K. Generalized projection discrepancy and its applications in experimental designs. Metrika 79, 19–35 (2016). https://doi.org/10.1007/s00184-015-0541-0
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DOI: https://doi.org/10.1007/s00184-015-0541-0
Keywords
- Projection discrepancy
- Generalized discrete discrepancy
- Generalized minimum aberration
- Lower bound
- Orthogonality