Advertisement

Journal of Statistical Theory and Practice

, Volume 6, Issue 3, pp 492–500 | Cite as

A Note on Near-Orthogonal Latin Hypercubes with Good Space-Filling Properties

Article

Abstract

Orthogonal Latin hypercubes (OLHs) are generally inflexible with respect to run sizes and the numbers of factors, and do not guarantee desirable space-filling properties. This article presents a fast algorithm to construct near-OLHs. The constructed near-OLHs achieve near-orthogonality among columns and good space-filling properties. These designs improve those of Cioppa and Lucas (2007) and those constructed by the OA-based approach of Lin et al. (2009) with respect to both orthogonality and space-filling properties.

AMS Classification

62K99 

Keywords

Algorithm Computer experiments Latin squares 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cioppa, T. M., and T. W. Lucas. 2007. Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics, 49, 45–55.MathSciNetCrossRefGoogle Scholar
  2. Fang, K. T., C. Ma, and P. Winker. 2000. Centered L 2 discrepancy of random sampling and Latin hypercube design, and construction of uniform designs. Math. Computation, 71, 275–296.MathSciNetCrossRefGoogle Scholar
  3. Georgiou, S. D. 2009. Orthogonal Latin hypercube designs from generalized orthogonal designs. J. Stat. Plan. Inference, 139, 1530–1540.MathSciNetCrossRefGoogle Scholar
  4. Hickernell, F. J. 1998. A generealized discrepancy and quadrature error bound. Math. Computation, 67, 299–322.MathSciNetCrossRefGoogle Scholar
  5. Johnson, M., L. Moore, and D. Ylvisaker. 1990. Minimax and maximin distance designs. J. Stat. Plan. Inference, 26, 131–148.MathSciNetCrossRefGoogle Scholar
  6. Lin, C. D., R. Mukerjee, and B. Tang. 2009. Construction of orthogonal and near orthogonal Latin hypercubes. Biometrika, 96, 243–247.MathSciNetCrossRefGoogle Scholar
  7. McKay, M. D., R. J. Beckman, and W. J. Conover. 1979. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21, 239–245.MathSciNetMATHGoogle Scholar
  8. Morris, M. D., and T. J. Mitchell. 1995. Exploratory designs for computer experiments. J. Stat. Plan. Inference, 43, 381–402.CrossRefGoogle Scholar
  9. Nguyen, N.-K. 1996. An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.CrossRefGoogle Scholar
  10. Nguyen, N.-K. 2008. A new class of orthogonal Latin hypercubes. Special volume in honour of Aloke Dey. Stat. Appl., 6, 119–123.Google Scholar
  11. Nguyen, N.-K., and D. K. J. Lin. 2011. A Note on small composite designs for sequential experimentation. J. Stat. Theory Pract., 5, 109–117.MathSciNetCrossRefGoogle Scholar
  12. Pang, F., M. Q. Liu, and D. K. J. Lin. 2009. A construction method for orthogonal Latin hypercube designs with prime power levels. Stat. Sin., 19, 1721–1728.MathSciNetMATHGoogle Scholar
  13. Steinberg, D. M., and D. K. J. Lin. 2006. A construction method for Latin hypercube designs. Biometrika, 93, 279–288.MathSciNetCrossRefGoogle Scholar
  14. Sun, F., M.Q. Liu, and D. K. J. Lin. 2009. Construction of orthogonal Latin hypercube designs. Biometrika, 96, 971–974.MathSciNetCrossRefGoogle Scholar
  15. Sun, F., M.Q. Liu, and D. K. J. Lin. 2010. Second-order orthogonal Latin hypercube designs with flexible run sizes. J. Stat. Plan. Inference, 140, 3235–3242.Google Scholar
  16. Yang, J. Y., and M. Q. Liu. 2012. Construction of orthogonal and near orthogonal Latin hypercubes from orthogonal designs. Stat. Sin., 22, 433–442.MATHGoogle Scholar
  17. Ye, K. Q. 1998. Orthogonal Latin hypercubes and their application in computer experiments. J. Am. Stat. Assoc., 93, 1430–1439.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.International School and Centre for High Performance ComputingVietnam National UniversityHanoiVietnam
  2. 2.Department of StatisticsPennsylvania State UniversityUniversity ParkUSA

Personalised recommendations