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A note on Lee discrepancy. (English) Zbl 1416.62451

Summary: The objective of this paper is to study the issue of Lee discrepancy [Y.-D. Zhou et al., Stat. Probab. Lett. 78, No. 13, 1933–1942 (2008; Zbl 1147.62065)], which can be used to measure the uniformity of fractional factorials. Here we present two improved lower bounds of Lee discrepancy of fractional factorials with two or three levels, and develop some links between Lee discrepancy and minimum moment aberration [H. Xu, Stat. Sin. 13, No. 3, 691–708 (2003; Zbl 1028.62063)].

MSC:

62K15 Factorial statistical designs
62K10 Statistical block designs
Full Text: DOI

References:

[1] Fang, K. T.; Wang, Y., Number-Theoretic Methods in Statistics (1994), Chapman and Hall: Chapman and Hall New York · Zbl 0925.65263
[2] Fang, K. T.; Ma, C. X.; Mukerjee, R., Uniformity in fractional factorials, (Fang, K. T.; Hickernell, F. J.; Niederreiter, H., Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (2002), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0994.62071
[3] Fang, K. T.; Qin, H., A note on construction of nearly uniform designs with large number of runs, Statist. Probab. Lett., 61, 215-224 (2003) · Zbl 1038.62069
[4] Fang, K. T.; Li, R.; Sudjianto, A., Design and Modeling for Computer Experiments (2005), Chapman and Hall: Chapman and Hall London
[5] Hickernell, F. J.; Liu, M. Q., Uniform designs limit aliasing, Biometrika, 89, 893-904 (2002) · Zbl 1036.62060
[6] Liu, M.Q., Qin, H., Xie, M.Y., 2005. Discrete discrepancy and its application in experimental designs. In: Contemporary Multivariate Analysis and Experimental Designs—In Celebration of Professor Kai Tai Fang’s 65th Birthday, pp. 73-88; Liu, M.Q., Qin, H., Xie, M.Y., 2005. Discrete discrepancy and its application in experimental designs. In: Contemporary Multivariate Analysis and Experimental Designs—In Celebration of Professor Kai Tai Fang’s 65th Birthday, pp. 73-88
[7] Qin, H., Zou, N., Chatterjee, K., 2008. Connection between uniformity and minimum moment aberration. Metrika (in press); Qin, H., Zou, N., Chatterjee, K., 2008. Connection between uniformity and minimum moment aberration. Metrika (in press) · Zbl 1433.62234
[8] Wang, Y.; Fang, K. T., A note on uniform distribution and experimental design, Chinese Sci. Bull., 26, 485-489 (1981) · Zbl 0493.62068
[9] Xu, H., Minimum moment aberration for nonregular designs and supersaturated designs, Statist. Sinica, 13, 691-708 (2003) · Zbl 1028.62063
[10] Zhou, Y. D.; Ning, J. H.; Song, X. B., Lee discrepancy and its applications in experimental designs, Statist. Probab. Lett., 78, 1933-1942 (2008) · Zbl 1147.62065
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