99
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Lower bound of average centered L2-discrepancy for U-type designs

, &
Pages 995-1008 | Received 19 Jul 2017, Accepted 20 Dec 2017, Published online: 17 Jan 2018

References

  • Bates, R. A., R. J. Buck, E. Riccomagno, and H. P. Wynn. 1996. Experimental design and observation for large systems. J. R. Stat. Soc. Ser. B 58:77–94.
  • Chatterjee, K., K. T. Fang, and H. Qin. 2006. A lower bound for centered L2-discrepancy on asymmetric factorials and its application. Metrika 63:243–55.
  • Chatterjee, K., K. T. Fang, and H. Qin. 2012. Some new lower bounds to centered and wrap-around L2-discrepancy. Statist. Probab. Lett. 82:1367–73.
  • Chen, H., H. Z. Huang, D. K. J. Lin, and M. Q. Liu. 2016. Uniform Sliced Latin Hypercube Designs. Applied Stochastic Models in Business and Industry 32:574–84.
  • Fang, K. T., and R. Mukerjee. 2000. A connection between uniformity and aberration in regular fractions of two-level factorials. Biometrika 87:93–198.
  • Fang, H. B., X. R. Chen, X. Y. Pei, S. Grant, and M. Tan. 2017. Experimental design and statistical analysis for three-drug combination studies. Statistical Methods in Medical Research 26:1261–80.
  • Fang, H. B., H. Z. Huang, R. Clarke, and M. Tan. 2016. Predicting multi-drug inhibition interactions based on signaling networks and single drug dose-response information. Journal of Computational Systems Biology 2(1):1–9.
  • Fang, K. T., R. Z. Li, and A. Sudjianto. 2006a. Design and modeling for computer experiments. New York: CRC Press.
  • Fang, K. T., X. Lu, and P. Winker. 2003. Lower bounds for centered and wrap-around L2-discrepancies and construction of uniform designs by threshold accepting. J. Complexity 19:692–711.
  • Fang, K. T., C. X. Ma, and P. Winker. 2002. Centered L2-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs. Math. Comput. 71:275–96.
  • Fang, K. T., D. Maringer, Y. Tang, and P. Winker. 2006b. Lower bounds and stochastic optimization algorithms for uniform designs with three or four levels. Math. Comput. 75:859–78.
  • Elsawah, M. A., and H. Qin. 2014. New lower bound for centered L2-discrepancy of four-level U-type designs. Statist. Probab. Lett. 93:65–71.
  • Elsawah, M. A., and H. Qin. 2015. Lower bound of centered L2-discrepancy for mixed two and three levels U-type designs. J. Stat. Plan. Inf. 161:1–11.
  • Hickernell, F. J. 1998. A generalised discrepancy and quadrature error bound. Math. Comput. 67:299–322.
  • Huang, H. Z., H. B. Fang, and M. Tan. 2017. Experimental design for multi-drug combination studies using signaling networks. Biometrics, DOI: 10.1111/biom.12777.
  • Huang, H. Z., D. K. J. Lin, M. Q. Liu, and J. F. Yang. 2016. Computer experiments with both qualitative and quantitative variables. Technometrics 58:495–507.
  • MacWilliams, F. J., and N. J. A. Sloane. 1977. The theory of error-correcting codes. Amsterdam: North-Holland.
  • Qin, H., S. L. Zhang, and K. T. Fang. 2006. Constructing uniform design with two- or three-level. Acta Math. Sci. Ser. B 26:451–59.
  • Tang, Y., and H. Q. Xu. 2013. An effective construction method for multi-level uniform designs. J. Stat. Plan. Inf. 143:1583–9.
  • Tang, Y., H. Q. Xu, and D. K. J. Lin. 2012. Uniform fractional factorial designs. Ann. Stat. 40:891–907.
  • Tan, M., H. B. Fang, H. Z. Huang, and Y. Yang. 2016. Design and statistical analysis of multidrug combinations in preclinical studies and clinical trials. In Statistical Applications from Clinical Trials and Personalized Medicine to Finance and Business Analytics, ed. J. Lin, B. Wang, X. Hu, K. Chen, and R. Liu, 215–234. New York & Switzerland: Springer.
  • Wang, Y., and K. T. Fang. 1981. A note on uniform distribution and experimental design. Chin. Sci. Bull. 26:485–9.
  • Xu, H. Q., and C. F. J. Wu. 2001. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Stat. 29:1066–77.
  • Yang, X., H. Chen, and M. Q. Liu. 2014. Resolvable orthogonal array-based uniform sliced Latin hypercube designs. Statist. Probab. Lett. 93:108–15.
  • Yang, X., G. J. Yang, and Y. J. Su. 2017. Uniform minimum moment aberration designs. Statist. Probab. Lett. (Accepted).
  • Zhong, W. J., F. F. Shao, and Y. Tang. 2017. Level permutation method for constructing mixed-level uniform designs under the wrap-around L2-discrepancy. Acta Mathematica Sinica, Chinese Series 4:557–68.

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.