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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cioppa, T. M., and T. W. Lucas. 2007. Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics, 49, 45–55.
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.
Georgiou, S. D. 2009. Orthogonal Latin hypercube designs from generalized orthogonal designs. J. Stat. Plan. Inference, 139, 1530–1540.
Hickernell, F. J. 1998. A generealized discrepancy and quadrature error bound. Math. Computation, 67, 299–322.
Johnson, M., L. Moore, and D. Ylvisaker. 1990. Minimax and maximin distance designs. J. Stat. Plan. Inference, 26, 131–148.
Lin, C. D., R. Mukerjee, and B. Tang. 2009. Construction of orthogonal and near orthogonal Latin hypercubes. Biometrika, 96, 243–247.
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.
Morris, M. D., and T. J. Mitchell. 1995. Exploratory designs for computer experiments. J. Stat. Plan. Inference, 43, 381–402.
Nguyen, N.-K. 1996. An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.
Nguyen, N.-K. 2008. A new class of orthogonal Latin hypercubes. Special volume in honour of Aloke Dey. Stat. Appl., 6, 119–123.
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.
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.
Steinberg, D. M., and D. K. J. Lin. 2006. A construction method for Latin hypercube designs. Biometrika, 93, 279–288.
Sun, F., M.Q. Liu, and D. K. J. Lin. 2009. Construction of orthogonal Latin hypercube designs. Biometrika, 96, 971–974.
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.
Yang, J. Y., and M. Q. Liu. 2012. Construction of orthogonal and near orthogonal Latin hypercubes from orthogonal designs. Stat. Sin., 22, 433–442.
Ye, K. Q. 1998. Orthogonal Latin hypercubes and their application in computer experiments. J. Am. Stat. Assoc., 93, 1430–1439.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nguyen, NK., Lin, D.K.J. A Note on Near-Orthogonal Latin Hypercubes with Good Space-Filling Properties. J Stat Theory Pract 6, 492–500 (2012). https://doi.org/10.1080/15598608.2012.695700
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1080/15598608.2012.695700