U-型设计的对称化L2-偏差的下界

数学物理学报 ›› 2022, Vol. 42 ›› Issue (6): 1802-1811.

U-型设计的对称化L₂-偏差的下界

雷轶菊¹(),欧祖军^2,*()

¹ 新乡学院数学与统计学院, 河南新乡 453003
² 吉首大学数学与统计学院, 湖南吉首 416000

收稿日期:2021-07-22 出版日期:2022-12-26 发布日期:2022-12-16
通讯作者: 欧祖军 E-mail:leiyiju2001@sina.com;ozj9325@mail.ccnu.edu.cn
作者简介:雷轶菊, E-mail: leiyiju2001@sina.com
基金资助:
国家自然科学基金(11961027);国家自然科学基金(12161040);国家自然科学基金(11701213);湖南省自然科学基金(2021JJ30550);湖南省自然科学基金(2020JJ4497)

Lower Bounds for the Symmetric L₂-Discrepancy of U-type Designs

Yiju Lei¹(),Zujun Ou^2,*()

¹ College of Mathematics and Statistics, Xinxiang University, Henan xinxiang 453003
² College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000

Received:2021-07-22 Online:2022-12-26 Published:2022-12-16
Contact: Zujun Ou E-mail:leiyiju2001@sina.com;ozj9325@mail.ccnu.edu.cn
Supported by:
the NSFC(11961027);the NSFC(12161040);the NSFC(11701213);the Natural Science Foundation of Hunan Province(2021JJ30550);the Natural Science Foundation of Hunan Province(2020JJ4497)

摘要/Abstract

摘要：

均匀设计是部分因子设计的主要方法之一, 已被广泛地应用于工业生产、系统工程、制药及其他自然科学中.各种偏差被用来度量部分因子设计的均匀性, 其关键的问题是寻找一个精确的偏差下界, 因为它可以作为衡量设计均匀性的标准.该文给出了4水平对称U-型设计的对称化L₂-偏差的下界, 以及2、3混水平和2、4混水平非对称U-型设计的对称化L₂-偏差的下界

关键词: U-型设计, 对称化L₂-偏差, 下界

Abstract:

Uniform design is one of the main methods of fractional factorials, which has been widely used in industrial production, systems engineering, pharmacy and other natural sciences. Various discrepancies are used to measure the uniformity of fractional factorials, the key is to find an accurate lower bound of the discrepancy, because it can be used as a benchmark which measures uniformity of design. In this paper, the lower bounds for the symmetric L₂-discrepancy on symmetrical U-type designs with four-level and asymmetrical U-type designs with two and three mixed levels and two and four mixed levels are abtained.

Key words: U-type design, Symmetric L₂-discrepancy, Lower bound

中图分类号:

O212.6

雷轶菊,欧祖军. U-型设计的对称化L₂-偏差的下界[J]. 数学物理学报, 2022, 42(6): 1802-1811.

Yiju Lei,Zujun Ou. Lower Bounds for the Symmetric L₂-Discrepancy of U-type Designs[J]. Acta mathematica scientia,Series A, 2022, 42(6): 1802-1811.

参考文献

1	Fang K T, Wang Y. Number-Theoretic Methods in Statistics. London: Chapman and Hall, 1994
2	Hickernell F J . A generalized discrepancy and quadrature erron bound. Mathematics of Computation, 1998, 67 (221): 299- 322
3	Hickernell F J. Lattice Rules: How well do they measure up?//Hellekalek P, Larche G. Random and Quasi-Random Point Sets. New York: Springer, 1998: 109-166
4	Hickernell F J , Liu M Q . Uniform designs limit aliasing. Biometrika, 2002, 89, 893- 904
5	Zhou Y D , Ning J H , Song X B . Lee discrepancy and its applications in experimental designs. Statistics & Probability Letters, 2008, 78, 1933- 1942
6	Chatterjee K , Qin H . Generalized discrete discrepancy and its application in experimental designs. Journal of Statistical Planning and Inference, 2011, 141, 951- 960
7	Fang K T , Mukerjee R . A connection between uniformity and aberration in regular fractions of two-level factorials. Biometrika, 2000, 87, 193- 198
8	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 2000. Berlin: Springer-Verlag, 2002: 232-241
9	Fang K T , Lu X , Winker P . Lower bounds for centered and wrap-around L₂-discrepancy and construction of uniform designs by threshold accepting. Journal of Complexity, 2003, 19, 692- 711
10	Chatterjee K , Fang K T , Qin H . Uniformity in factorial designs with mixed levels. Journal of Statistical Planning and Inference, 2005, 128, 593- 607
11	Chatterjee K , Fang K T , Qin H . A lower bound for centered L₂-discrepancy on asymmetric factorials and its application. Metrika, 2006, 63, 243- 255
12	Wang Z H , Qin H , Chatterjee K . Lower bounds for the symmetric L₂-discrepancy and their application. Communications in Statistics-Theory and Methods, 2007, 36, 2413- 2423
13	Qin H , Li D . Connection between uniformity and orthogonality for symmetrical factorial designs. Journal of Statistical Planning and Inference, 2006, 136, 2770- 2782
14	Qin H , Fang K T . Discrete discrepancy in factorial designs. Metrika, 2004, 60, 59- 72
15	Fang K T , Maringer D , Tang Y , Winker P . Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels. Mathematics of Computation, 2006, 75, 859- 878
16	Chatterjee K , Ou Z J , Phoa F K H , Qin H . Uniform four-level designs from two-level designs: a new look. Statistica Sinica, 2017, 27, 171- 186
17	覃红, 欧祖军, ChatterjeeKashinath. 四水平计算机试验设计的构造. 中国科学: 数学, 2017, 47 (9): 1089- 1100
17	Qin H , Ou Z J , Chatterjee K . Construction of four-level designs for computer experiments. Scientia Sinica Mathematica, 2017, 47 (9): 1089- 1100
18	Hu L P , Li H Y , Ou Z J . Constructing optimal four-level designs via gray map code. Metrika, 2019, 82 (5): 573- 587
19	Qin H , Zhang S L , Fang K T . Constructing uniform design with two or three-level. Acta Mathematica Scientia, 2006, 26, 451- 459
20	Zhou Y D , Ning J H . Lower bounds of wrap-around L₂-discrepancy and relationships between MLHD and uniform design with a large size. Journal of Statistical Planning and Inference, 2008, 138, 2330- 2339
21	Zhang Q H , Wang Z H , Hu J W , Qin H . A new lower bound for wrap-around L₂-discrepancy on two and three mixed level factorials. Statistics & Probability Letters, 2015, 96, 133- 140
22	雷轶菊, 欧祖军. 三水平U-型设计在对称化L₂-偏差下的下界. 应用数学学报, 2018, 41 (1): 138- 144
22	Lei Y J , Ou Z J . Lower bound of symmetric L₂-discrepancy on three-level U-type designs. Acta Mathematicae Applicatae Sinca,2018, 41 (1): 138- 144
23	Zhou Y D , Fang K T , Ning J H . Mixture discrepancy for quasi-random points sets. Journal of Complexity, 2013, 29, 283- 301

[1]	杨莹,周锐,朱世辉. 带磁场的广义Zakharov模型的奇异解[J]. 数学物理学报, 2022, 42(1): 70-85.
[2]	雷轶菊,欧祖军,赵国喜. 混水平列扩充设计的混偏差的下界[J]. 数学物理学报, 2021, 41(3): 882-891.
[3]	覃思乾,凌征球,周泽文. 一类抛物方程爆破时间下界的确定方法与有效性分析[J]. 数学物理学报, 2019, 39(5): 1033-1040.
[4]	孙宝燕. 具有非局部源的p-Laplace方程解的爆破时间下界估计[J]. 数学物理学报, 2018, 38(5): 911-923.
[5]	马羚未, 方钟波. 具有加权非局部源和Robin边界条件的反应-扩散方程解的爆破时间下界[J]. 数学物理学报, 2017, 37(1): 146-157.
[6]	凌征球, 王泽佳. 带具有耗散梯度项的p-Laplace方程解的爆破问题[J]. 数学物理学报, 2016, 36(5): 958-964.
[7]	何跃. 正Ricci曲率的紧流形上第一特征值下界的新估计[J]. 数学物理学报, 2016, 36(2): 215-230.
[8]	孙昭洪, 张玮, 贺铁山, 高川翔. 一类弱二次Hamilton系统的同宿解的多重性结果[J]. 数学物理学报, 2015, 35(2): 364-372.
[9]	丁夏畦. 一个二次泛函的估计(I)——纪念李国平院士吴新谋教授诞辰100周年[J]. 数学物理学报, 2010, 30(5): 1347-1353.
[10]	王光. 解析函数模的下界问题[J]. 数学物理学报, 1999, 19(3): 333-337.
[11]	许进. 自补图中的三角形[J]. 数学物理学报, 1996, 16(S1): 38-41.

U-型设计的对称化L₂-偏差的下界

Lower Bounds for the Symmetric L₂-Discrepancy of U-type Designs

RichHTML

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 11

Metrics

本文评价

推荐阅读 0