156
Views
17
CrossRef citations to date
0
Altmetric
Articles

Asymmetric uniform designs based on mixture discrepancy

&
Pages 2280-2294 | Received 22 Mar 2015, Accepted 07 Jan 2016, Published online: 02 Feb 2016

References

  • S.W. Cheng and K.Q. Ye, Geometric isomorphism and minimum aberration for factorial designs with quantitative factors, Ann. Statist. 32 (2004), pp. 2168–2185. doi: 10.1214/009053604000000599
  • A.M. Elsawah and H. Qin, New lower bound for centered L2-discrepancy of four-level U-type designs, Statist. Probab. Lett. 93 (2014), pp. 65–71. doi: 10.1016/j.spl.2014.06.008
  • A.M. Elsawah and H. Qin, Lee discrepancy on symmetric three-level combined designs, Statist. Probab. Lett. 96 (2015a), pp. 273–280. doi: 10.1016/j.spl.2014.09.027
  • A.M. Elsawah and H. Qin, Lower bound of centered L2-discrepancy for mixed two and three levels U-type designs, J. Statist. Plann. Infer. 161 (2015b), pp. 1–11. doi: 10.1016/j.jspi.2014.12.007
  • A.M. Elsawah and H. Qin, A new strategy for optimal foldover two-level designs, Statist. Probab. Lett. 103 (2015c), pp. 116–126. doi: 10.1016/j.spl.2015.04.020
  • A.M. Elsawah and H. Qin, Mixture discrepancy on symmetric balanced designs, Statist. Probab. Lett. 104 (2015d), pp. 123–132. doi: 10.1016/j.spl.2015.05.007
  • K.T. Fang, The uniform design: Application of number-theoretic methods in experimental design, Acta Math. Appl. Sin. 3 (1980), pp. 363–372.
  • K.T. Fang, R.Z. Li, and A. Sudjianto, Design and Modeling for Computer Experiments, Chapman and Hall/CRC, New York, 2006.
  • K.T. Fang, X. Lu, and P. Winker, Lower bounds for centered and wrap-around L2-discrepancies and construction of uniform designs by threshold accepting, J. Complexity 19 (2003), pp. 692–711. doi: 10.1016/S0885-064X(03)00067-0
  • F.J. Hickernell, A generalized discrepancy and quadrature error bound, Math. Comput. Am. Math. Soc. 67 (1998a), pp. 299–322. doi: 10.1090/S0025-5718-98-00894-1
  • F.J. Hickernell, Lattice rules: How well do they measure up? in Random and Quasi-Random Point Sets, P. Hellekalek and G. Larcher, eds., Lecture Notes in Statistics 138, Springer, New York, 1998, pp. 109–166.
  • X. Ke, R. Zhang, and H.J. Ye, Two- and three-level lower bounds for mixture L2-discrepancy and construction of uniform designs by threshold accepting, J. Complexity 31 (2015), pp. 741–753. doi: 10.1016/j.jco.2015.01.002
  • Y. Wang and K.T. Fang, A note on uniform distribution and experimental design, Chinese Sci. Bull. 26 (1981), pp. 485–489.
  • H. Weyl, Üer die Gleichverteilung der Zahlem mod Eins, Math. Ann. 77 (1916), pp. 313–352. doi: 10.1007/BF01475864
  • P. Winker, Optimization Heuristics in Econometrics: Applications of Threshold Accepting, Wiley, Chichester, 2001.
  • P. Winker and K.T. Fang, Application of threshold accepting to the evaluation of the discrepancy of a set of points, SIAM J. Numer. Anal. 34 (1997), pp. 2028–2042. doi: 10.1137/S0036142995286076
  • Y.D. Zhou, K.T. Fang, and J.H. Ning, Mixture discrepancy for quasi-random point sets, J. Complexity 29 (2013), pp. 283–301. doi: 10.1016/j.jco.2012.11.006
  • Y.D. Zhou and H.Q. Xu, Space-filling fractional factorial designs, J. Amer. Statist. Assoc. 507 (2014), pp. 1134–1144. doi: 10.1080/01621459.2013.873367

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.