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Centered  -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs
Author(s):
Kai-Tai
Fang;
Chang-Xing
Ma;
Peter
Winker.
Journal:
Math. Comp.
71
(2002),
275-296.
MSC (2000):
Primary 68U07;
Secondary 65D17, 62K99
Posted:
October 16, 2000
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Abstract:
In this paper properties and construction of designs under a centered version of the  -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.
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Additional 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
DOI:
10.1090/S0025-5718-00-01281-3
PII:
S 0025-5718(00)01281-3
Keywords:
Uniform design,
Latin hypercube design,
threshold accepting heuristic,
quasi-Monte Carlo methods
Received by editor(s):
July 20, 1999
Received by editor(s) in revised form:
February 25, 2000
Posted:
October 16, 2000
Additional Notes:
This work was partially supported by a Hong Kong RGC-grant and SRCC of Hong Kong Baptist University.
Copyright of article:
Copyright
2000,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Fang KT, Qin H, A note on construction of nearly uniform designs with large number of runs, STATISTICS & PROBABILITY LETTERS 61 (2003), 215-224 .
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