Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1802-1811.
Previous Articles Next Articles
Lower Bounds for the Symmetric L2-Discrepancy of U-type Designs
Yiju Lei1(
),Zujun Ou2,*()
- 1 College of Mathematics and Statistics, Xinxiang University, Henan xinxiang 453003
2 College of Mathematics and Statistics, Jishou University, Hunan Jishou 416000
-
Received:2021-07-22Online:2022-12-26Published: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)
CLC Number:
- O212.6
Cite this article
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.
share this article
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
| 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
doi: 10.1090/S0025-5718-98-00894-1 |
| 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
doi: 10.1093/biomet/89.4.893 |
| 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
doi: 10.1016/j.jspi.2010.08.014 |
| 7 |
Fang K T , Mukerjee R . A connection between uniformity and aberration in regular fractions of two-level factorials. Biometrika, 2000, 87, 193- 198
doi: 10.1093/biomet/87.1.193 |
| 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
doi: 10.1016/S0885-064X(03)00067-0 |
| 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
doi: 10.1016/j.jspi.2003.12.012 |
| 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
doi: 10.1007/s00184-005-0015-x |
| 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
doi: 10.1080/03610920701232667 |
| 13 |
Qin H , Li D . Connection between uniformity and orthogonality for symmetrical factorial designs. Journal of Statistical Planning and Inference, 2006, 136, 2770- 2782
doi: 10.1016/j.jspi.2004.11.005 |
| 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 |
| 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
doi: 10.1007/s00184-018-0685-9 |
| 19 |
Qin H , Zhang S L , Fang K T . Constructing uniform design with two or three-level. Acta Mathematica Scientia, 2006, 26, 451- 459
doi: 10.1016/S0252-9602(06)60069-6 |
| 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
doi: 10.1016/j.jspi.2007.10.001 |
| 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 |
| 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
doi: 10.1016/j.jco.2012.11.006 |
| [1] | Ying Yang,Rui Zhou,Shihui Zhu. On the Singular Solutions to a Generalized Magnetic Zakharov Model [J]. Acta mathematica scientia,Series A, 2022, 42(1): 70-85. |
| [2] | Yiju Lei,Zujun Ou,Guoxi Zhao. Lower Bounds on Mixture-Discrepancy of the Mixed-Level Column Augmented Design [J]. Acta mathematica scientia,Series A, 2021, 41(3): 882-891. |
| [3] | Siqian Qin,Zhengqiu Ling,Zewen Zhou. Some Methods for Determining the Lower Bound of Blow-up Time in a Parabolic Problem and Effectiveness Analysis [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1033-1040. |
| [4] | Baoyan Sun. Lower Bound of Blow-Up Time for a p-Laplacian Equation with Nonlocal Source [J]. Acta mathematica scientia,Series A, 2018, 38(5): 911-923. |
| [5] | Ma Lingwei, Fang Zhongbo. Lower Bounds of Blow-up Time for a Reaction-Diffusion Equation with Weighted Nonlocal Sources and Robin Type Boundary Conditions [J]. Acta mathematica scientia,Series A, 2017, 37(1): 146-157. |
| [6] | Ling Zhengqiu, Wang Zejia. Blow-Up Questions of Solutions to a Class of p-Laplace Equation with Dissipative Gradient Term [J]. Acta mathematica scientia,Series A, 2016, 36(5): 958-964. |
| [7] | He Yue. New Estimates of Lower Bound for the First Eigenvalue on Compact Manifolds with Positive Ricci Curvature [J]. Acta mathematica scientia,Series A, 2016, 36(2): 215-230. |
| [8] | Sun Zhaohong, Zhang Wei, He Tieshan, Gao Chuanxiang. Multiplicity Result for Homoclinic Solutions to A Class of Subquadratic Hamiltonian Systems [J]. Acta mathematica scientia,Series A, 2015, 35(2): 364-372. |
| [9] | DING Xia-Qi. The Estimate of a Quadratic Functional [J]. Acta mathematica scientia,Series A, 2010, 30(5): 1347-1353. |
| [10] | Yan Xia; Yu Dan; Li Guoying. Bound of Parametric Functions and Its Applications [J]. Acta mathematica scientia,Series A, 2007, 27(2): 229-239. |
|