五水平U型设计在可卷型L2-偏差下的新下界

doi:10.13438/j.cnki.jdzk.2022.04.002

吉首大学学报（自然科学版） ›› 2022, Vol. 43 ›› Issue (4): 7-10.DOI: 10.13438/j.cnki.jdzk.2022.04.002

五水平U型设计在可卷型L₂-偏差下的新下界

胡柳平,裴武,周昱,欧祖军

(1.华中师范大学数学与统计学学院，湖北武汉 430079;2.吉首大学师范学院，湖南吉首 416000;3.吉首大学数学与统计学院，湖南吉首 416000)

出版日期:2022-07-25 发布日期:2022-10-28
通讯作者: 欧祖军(1979—),男,湖南宜章人,吉首大学数学与统计学院教授,博士,主要从事概率统计和试验设计研究.
作者简介:胡柳平（1987—），男，湖南邵阳人，吉首大学师范学院助教，硕士，主要从事试验设计研究
基金资助:
国家自然科学基金资助项目(11961027,12161040)；湖南省教育厅科学研究项目(21C0370)

New Lower Bound of Wrap-Around L2-Discrepancy for Five-Level U-Type Designs

HU Liuping,PEI Wu,ZHOU Yu,OU Zujun

(1.College of Mathematics and Statistics,Central China Normal University,Wuhan 430079,China;2.Normal College,Jishou University,Jishou 416000,Hunan China;3.College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2022-07-25 Published:2022-10-28

摘要/Abstract

摘要：通过变换得到了五水平U型设计可卷型L₂-偏差的一个新表达式,基于该表达式和数学不等式得到了该偏差的一个新下界.

关键词： 五水平, 可卷型L₂-偏差, 下界

Abstract: We obtain a new expression of wrap-around L₂-discrepancy for five-level U-type designs.A new lower bound of wrap-around L₂-discrepancy can be derived via the expression and a mathematical inequality.

Key words: five-level, wrap-around L₂-discrepancy, lower bound

胡柳平, 裴武, 周昱, 欧祖军. 五水平U型设计在可卷型L₂-偏差下的新下界[J]. 吉首大学学报（自然科学版）, 2022, 43(4): 7-10.

HU Liuping, PEI Wu, ZHOU Yu, OU Zujun. New Lower Bound of Wrap-Around L2-Discrepancy for Five-Level U-Type Designs[J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(4): 7-10.

参考文献

[1] HICKERNELL FRED J.A Generalized Discrepancy and Quadrature Error Bound[J].Mathematics of Computation,1998,67(221):299-322.
[2] FANG Kaitai,MA Changxing,MUKERJEE RAHUL.Uniformity in Fractional Factorials[M]∥ FANG Kaitai,HICKERNELL FRED J,NIEDERREITER HARAL,Eds.Monte Carlo and Quasi-Monte Carlo Methods 2000.Berlin:Springer-Verlag,2002:232-241.
[3] FANG Kaitai,LU Xuan,WINKER PETER.Lower Bounds for Centered and Wrap-Around L2-Discrepancy and Construction of Uniform Designs by Threshold Accepting[J].Journal of Complexity,2003,19(5):692-711.
[4] QIN Hong,ZHANG Shangli,FANG Kaitai.Constructing Uniform Design with Two-or Three-Level[J].Acta Mathematica Scientia,2006,26(3):451-459.
[5] CHATTERJEE KASHINATH,LI Zhaohai,QIN Hong.Some New Lower Bounds to Centered and Wrap-Around L2-Discrepancies[J].Statistics & Probability Letters,2012,82(7):1367-1373.
[6] CHATTERJEE KASHINATH,FANG Kaitai,QIN Hong.Uniformity in Factional Designs with Mixed Levels[J].Journal of Statistical Planning and Inference,2005,128(2):593-607.
[7] ZHANG Qionghui,WANG Zhenghong,HU Jianwei,et al.A New Lower Bound for Wrap-Around L2-Discrepancy on Two and Three Mixed Level Factorials[J].Statistics & Probability Letters,2015,96:133-140.
[8] FANG Kaitai,TANG Yu,YIN Jianxing.Lower Bounds for Wrap-Around L2-Discrepancy and Constructions of Symmetrical Uniform Designs[J].Journal of Complexity,2005,21(5):757-771.
[9] ZHOU Yongdao,NING Jianhui.Lower Bounds of the Wrap-Around L2-Discrepancy and Relationships Between MLHD and Uniform Design with a Large Size[J].Journal of Statistical Planning and Inference,2008,138(8):2330-2339.
[10] HU Liuping,CHATTERJEE KASHINATH,LIU Jiaqi,et al.New Lower Bound for Lee Discrepancy of Asymmetrical Factorials[J].Statistical Papers,2020,61(4):1763-1772.

五水平U型设计在可卷型L₂-偏差下的新下界

New Lower Bound of Wrap-Around L2-Discrepancy for Five-Level U-Type Designs

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