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References (22)
-
F. Hickernell (1998)
Lattice rules: how well do they measure up? in random and quasi-random point sets -
(2010)
Application of minimum projection uniformity in complementary designs -
Aijun Zhang, K. Fang, Runze Li, A. Sudjianto (2005)
Majorization framework for balanced lattice designsAnnals of Statistics, 33
-
KT Fang, CX Ma, R Mukerjee (2002)
Monte Carlo and Quasi-Monte Carlo Methods -
KT Fang, X Lu, P Winker (2003)
Lower bounds for centered and wrap-around L 2-discrepancies and construction of uniform designs by threshold acceptingJ. Complexity, 19
-
Yong-Dao Zhou, J. Ning, Xie-Bing Song (2008)
Lee discrepancy and its applications in experimental designsStatistics & Probability Letters, 78
-
HQ Xu, CFJ Wu (2001)
Generalized minimum aberration for asymmetrical fractional factorial designsAnn. Statist., 29
-
K. Fang, Xuan Lu, P. Winker (2003)
Lower bounds for centered and wrap-around L2-discrepancies and construction of uniform designs by threshold acceptingJ. Complex., 19
-
(1946)
The design of optimum multi-factorial experiments -
Hongquan Xu, Ching-Shui Cheng (2008)
A Complementary Design Theory for Doubling -
D. Lin (1993)
A new class of supersaturated designsTechnometrics, 35
-
F. Hickernell (1998)
A generalized discrepancy and quadrature error boundMath. Comput., 67
-
P. Hellekalek, G. Larcher, J. Beck (1998)
Random and Quasi-Random Point Sets -
Jiju Antony (2014)
Fractional factorial designs -
Shangli Zhang, H. Qin (2006)
Minimum projection uniformity criterion and its applicationStatistics & Probability Letters, 76
-
K. Fang, R. Mukerjee (2000)
A connection between uniformity and aberration in regular fractions of two-level factorialsBiometrika, 87
-
K. Fang, Chang-Xing Ma, R. Mukerjee (2002)
Uniformity in Fractional Factorials -
H. Qin, K. Fang (2004)
Discrete discrepancy in factorial designsMetrika, 60
-
Hegang Chen, Ching-Shui Cheng (2006)
Doubling and projection: A method of constructing two-level designs of resolution IVAnnals of Statistics, 34
-
BY Mukerjee, WU C.F.JEFF (1995)
On the existence of saturated and nearly saturated asymmetrical orthogonal arraysAnnals of Statistics, 23
-
K. Fang, H. Qin (2005)
Uniformity pattern and related criteria for two-level factorialsScience in China Series A: Mathematics, 48
-
A. Fries, W. Hunter (1980)
Minimum Aberration 2 k–p DesignsTechnometrics, 22
- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-014-0419-3
- Publisher site
- See Article on Publisher Site
Abstract
In constructing two-level fractional factorial designs, the so-called doubling method has been employed. In this paper, we study the problem of uniformity in double designs. The centered L 2-discrepancy is employed as a measure of uniformity. We derive results connecting the centered L 2-discrepancy value of D(X) and generalized wordlength pattern of X, which show the uniformity relationship between D(X) and X. In addition, we also obtain lower bounds of centered L 2-discrepancy value of D(X), which can be used to assess uniformity of D(X).
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Nov 6, 2014