TY - JOUR
T1 - Wrap-around L2-discrepancy of random sampling, latin hypercube and uniform designs
AU - Fang, Kai Tai
AU - Ma, Chang Xing
N1 - Funding Information:
This work was partially supported by Hong Kong RGC-Grant RC/98-99/Gen 370 and the SRCC of Hong Kong Baptist University.
PY - 2001/12
Y1 - 2001/12
N2 - For comparing random designs and Latin hypercube designs, this paper considers 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.
AB - For comparing random designs and Latin hypercube designs, this paper considers 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.
KW - Latin hypercube design
KW - quasi Monte-Carlo methods
KW - threshold accepting heuristic
KW - uniform design
KW - wrap-around discrepancy
UR - http://www.scopus.com/inward/record.url?scp=0035704144&partnerID=8YFLogxK
U2 - 10.1006/jcom.2001.0589
DO - 10.1006/jcom.2001.0589
M3 - Journal article
AN - SCOPUS:0035704144
SN - 0885-064X
VL - 17
SP - 608
EP - 624
JO - Journal of Complexity
JF - Journal of Complexity
IS - 4
ER -