Centered $L_2$-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs
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- by Kai-Tai Fang, Chang-Xing Ma and Peter Winker;
- Math. Comp. 71 (2002), 275-296
- DOI: https://doi.org/10.1090/S0025-5718-00-01281-3
- Published electronically: October 16, 2000
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Abstract:
In this paper properties and construction of designs under a centered version of the $L_2$-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.References
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Bibliographic Information
- Kai-Tai Fang
- Affiliation: Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong; and Chinese Academy of Sciences, Beijing, China
- Email: ktfang@math.hkbu.edu.hk
- Chang-Xing Ma
- Affiliation: Department of Statistics, Nankai University, Tianjin, China
- Email: cxma@nankai.edu.cn
- Peter Winker
- Affiliation: Department of Economics, University of Mannheim, 68131 Mannheim, Germany
- Email: Peter.Winker@vwl.uni-mannheim.de
- Received by editor(s): July 20, 1999
- Received by editor(s) in revised form: February 25, 2000
- Published electronically: October 16, 2000
- Additional Notes: This work was partially supported by a Hong Kong RGC-grant and SRCC of Hong Kong Baptist University.
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 71 (2002), 275-296
- MSC (2000): Primary 68U07; Secondary 65D17, 62K99
- DOI: https://doi.org/10.1090/S0025-5718-00-01281-3
- MathSciNet review: 1863000