折叠反转设计的中心化L2偏差值的一些下界

数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1555-1561.

折叠反转设计的中心化L₂偏差值的一些下界

雷轶菊^1,2|覃红²|邹娜²

1.新乡学院数学系河南新乡 453000|2.华中师范大学统计系武汉 430079

收稿日期:2008-09-14 修回日期:2010-01-09 出版日期:2010-12-25 发布日期:2010-12-25
基金资助:
国家自然科学基金(10671080)和教育部新世纪优秀人才支持计划(06-672)资助

Some Lower Bounds of Centered L₂-discrepancy on Foldover Designs

LEI Yi-Ju^1,2, QIN Hong², ZOU Na²

1.Department of Mathematics, Xinxiang College, Henan |Xinxiang 453000|2.Department of Statistics, Central China Normal University, Wuhan 430079

Received:2008-09-14 Revised:2010-01-09 Online:2010-12-25 Published:2010-12-25
Supported by:
国家自然科学基金(10671080)和教育部新世纪优秀人才支持计划(06-672)资助

摘要/Abstract

摘要：

在二水平因子跟随试验中, 折叠反转技术是一种非常典型的方法和技巧. 这种技术通过折叠反转初始设计的一个或多个因子的水平符号, 可以获得一个具有很好统计推断性质的新设计(称为折叠反转设计). 初始设计与其折叠反转设计组合在一起所形成的新设计称为组合设计. 该文在完全折叠反转方案和部分折叠反转方案下分别得到了组合设计在中心化$L_2$偏差下的一些下界. 所得到的这些下界可以作为寻找最优折叠反转方案的一个标准, 因此, 该文的结果给出了用均匀性准则来寻找最优折叠反转方案的理论依据, 进一步说明了均匀性在因子设计中的有用性.

关键词: 中心化L₂偏差, 最优折叠反转方案, 均匀性

Abstract:

Foldover is a classic technique that reverses the sign(s) of one or more factors in the initial design for the follow-up experiment (called a foldover design). The full design obtained by joining the runs in the foldover design to those of the initial design is called a combined design. In this paper, under the full foldover plan and fractional foldover plans, some lower bounds of the combined designs in terms of centered L₂ discrepancy are obtained, which can be used as a benchmark for searching optimal foldover plans. The results provide a theoretical justification for optimal foldover plans based on uniformity criterion.

Key words: Centered L₂-discrepancy, Optimal foldover plan, Uniformity

中图分类号:

62K15

雷轶菊, 覃红, 邹娜. 折叠反转设计的中心化L₂偏差值的一些下界[J]. 数学物理学报, 2010, 30(6): 1555-1561.

LEI Yi-Ju, QIN Hong, ZOU Na. Some Lower Bounds of Centered L₂-discrepancy on Foldover Designs[J]. Acta mathematica scientia,Series A, 2010, 30(6): 1555-1561.

参考文献

[1] Box G E P, Hunter W G, Hunter J S. Statistics for Experimenters. New York: Wiley, 1978

[2] Chatterjee K, Fang K T, Qin H. Uniformity in factional designs with mixed levels. J Statist Plann Infer, 2005, 128: 593--607

[3] Fang K T, Lin D K J, Qin H. A note on optimal foldover design. Statistics $\&$ Probability Letters, 2003, 62: 245--250

[4] Fang K T, Lu X, Winker P. Lower bounds for centered and wrap-around L₂-discrepancies and construction of uniform designs by threshold accepting. J Complexity, 2003, 19: 692--711

[5] Fang K T, Ma C X, Mukerjee R. Uniformity in Fractional Factorials. Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Berlin: Springer-Verlag

[6] Fang K T, Mukerjee R. A connection between uniformity and aberration in regular fractions of two-level factorials. Biometrika, 2000, 87: 193--198

[7] Fang K T, Tang Y, Yin J X. Lower bounds of various criteria in experimental designs. J Statist Plann Infer, 2008, 138: 184--195

[8] Hickernell F J. A generalized discrepancy and quadrature error bound. Mathematics of Computation, 1998, 67: 299--322

[9] Li H, Mee R W. Better foldover fractions for resolution III 2^k-p designs. Technometrics, 2002, 44: 278--283

[10] Li W, Lin D K J. Optimal foldover plans for two-level fractional factorial designs. Technometrics, 2003, 45: 142--149

[11] Li W, Lin D K J, Ye K Q. Optimal foldover plans for non-regular orthogonal designs. Technometrics, 2003, 45: 347--351

[12] Lin D K J. A new class of supersaturated designs. Technometrics, 1993, 35: 28--31

[13] Montgomery D C, Runger G C. Foldovers of 2^k-presolution IV experimental designs. J Quality Tech, 1996, 28: 446--450

[14] Mukerjee R, Wu C F J. On the existence of saturated and nearly saturated asymmetrical orthogonal arrays. Ann Statist, 1995, 23: 2102--2115

[15] Wu C F J, Hamada M. Experiments Planning, Analysis, and Parameter Design Optimization. New York: A Wiely-interscience Publication, 2000

[16] Zhang A J, Fang K T, Li R, Sudjianto A. Majorization framework for balanced lattice designs. Ann Statist, 2005, 33: 2837--2853

折叠反转设计的中心化L₂偏差值的一些下界

Some Lower Bounds of Centered L₂-discrepancy on Foldover Designs

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

Metrics

本文评价

推荐阅读 0

[1]	雷轶菊, 赵守娟. (s^r)×sⁿ正规部分因子设计最优区组和折叠反转方案[J]. 数学物理学报, 2013, 33(4): 627-635.
[2]	胡东红, 李德华, 王祖喜. 均匀性度量的势函数模型[J]. 数学物理学报, 2003, 23(5): 607-612.
[3]	胡东红, 李德华, 王祖喜. 均匀性度量中的密集性偏差与稀疏性偏差[J]. 数学物理学报, 2002, 22(1): 128-134.