NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS

Shuo SONG; Qionghui ZHANG; Na ZOU; Hong QIN

doi:10.1016/S0252-9602(16)30109-6

Acta mathematica scientia, Series B >

2016 , Vol. 36 >Issue 6: 1832 - 1840

DOI: https://doi.org/10.1016/S0252-9602(16)30109-6

Articles

NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS

Shuo SONG ,
Qionghui ZHANG ,
Na ZOU ,
Hong QIN

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1. College of Science, Wuhan University of Science and Technology, Wuhan 430065, China;
2. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
3. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

Received date: 2015-01-24

Revised date: 2016-05-03

Online published: 2016-12-25

Supported by

The third author was supported by the National Natural Science Foundation of China (11301546). The fourth author is supported by the National Natural Science Foundation of China (11271147, 11471136).

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Abstract

The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.

Key words： U-type design; Lee discrepancy; uniform design; lower bound

Cite this article

Shuo SONG , Qionghui ZHANG , Na ZOU , Hong QIN . NEW LOWER BOUNDS FOR LEE DISCREPANCY ON TWO AND THREE MIXED LEVELS FACTORIALS[J]. Acta mathematica scientia, Series B, 2016 , 36(6) : 1832 -1840 . DOI: 10.1016/S0252-9602(16)30109-6

References

[1] Chatterjee K, Li Z H, Qin H. Some new lower bounds to centered and wrap-around L₂-discrepancies. Statist Probab Letters, 2012, 82:1367-1373
[2] Chatterjee K, Qin H, Zou N. Lee discrepancy on asymmetrical factorials with two- and three-levels. Science China Mathematics, 2012, 55:663-670
[3] Elsawah M A, Qin H. New lower bound for centered L₂-discrepancy of four-level U-type designs. Statist Probab Letters, 2014, 93:65-71
[4] Fang K T, Li R, Sudjianto A. Design and Modelling for Computer Experiments. London:Chapman and Hall, 2005
[5] Zhou Y D, Ning J H, Song X B. Lee discrepancy and its applications in experimental designs. Statist Probab Letters, 2008, 78:1933-1942
[6] Zou N, Ren P, Qin H. A note on Lee discrepancy. Statist Probab Letters, 2009, 79:496-500
[7] Zou N, Qin H. Some properties of double designs in terms of Lee discrepancy. Acta Matematica Scientia, accepted, 2016

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