Wrap-Around L2-Discrepancy of Random Sampling, Latin Hypercube and Uniform Designs |
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Authors: | Kai-Tai Fang Chang-Xing Ma |
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Institution: | Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, f1;Chinese Academy of Sciences, Beijing, China, f2;Department of Statistics, Nankai University, Tianjin, 300071, China, f3 |
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Abstract: | For comparing random designs and Latin hypercube designs, this paper con- siders a wrap-around version of the L2-discrepancy (WD). The theoretical expectation and variance of this discrepancy are derived for these two designs. The expectation and variance of Latin hypercube designs are significantly lower than those of the corresponding random designs. We also study construction of the uniform design under the WD and show that one-dimensional uniform design under this discrepancy can be any set of equidistant points. For high dimensional uniform designs we apply the threshold accepting heuristic for finding low discrepancy designs. We also show that the conjecture proposed by K. T. Fang, D. K. J. Lin, P. Winker, and Y. Zhang (2000, Technometrics) is true under the WD when the design is complete. |
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Keywords: | Latin hypercube design quasi Monte-Carlo methods threshold accepting heuristic uniform design wrap-around discrepancy |
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