Lower bounds for centered and wrap-around L2-discrepancies and construction of uniform designs by threshold accepting

Journal of Complexity

Volumn 19, Issue 5, 2003, Pages 692-711

  Fang, Kai Tai ^a   Lu, Xuan ^b   Winker, Peter ^c  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b TSINGHUA UNIVERSITY   (China)

^c UNIVERSITY OF ERFURT   (Germany)

Author keywords

Discrepancy; Hamming distance; Orthogonality; Threshold accepting; Uniform design

Indexed keywords

EID: 0141838172     PISSN: 0885064X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0885-064X(03)00067-0     Document Type: Article

References (15)

1. R. Bates, R. Buck, E. Riccomagno, H.P. Wynn, Experimental design and observations for large systems, J. Roy. Statist. Soc. B 57 (1996) 77-94.
2. K.-T. Fang, D.K.J. Lin, P. Winker, Y. Zhang, Uniform design: theory and application, Technometrics 42 (2000) 237-248.
3. 2 discrepancy of random sampling and latin hypercube design, and construction of uniform designs, Math. Comput. 71 (2002) 275-296.
4. K.-T. Fang, R. Mukerjee, A connection between uniformity and aberration in regular fractions of two-level factorials, Biometrika 87 (2000) 193-198.
5. K.-T. Fang, W.C. Shiu, J.X. Pan, Uniform designs based on latin squares, Statist. Sin. 9 (1999) 905-912.
6. K.-T. Fang, Y. Wang, Applications of Number Theoretic Methods in Statistics, Chapman S Hall, London, 1994.
7. R.W. Hamming, Error detecting and error correcting codes, Bell System Tech. J. 29 (1950) 147-160.
8. F.J. Hickernell, Lattice rules: how well do they measure up, in: P. Hellekalek, G. Larcher (Eds.), Random and Quasi-Random Point Sets, Springer, New York, 1998, pp. 106-166.
9. F.J. Hickernell, A generalized discrepancy and quadratic error bound, Math. Comput. 67 (1998) 299-322.
10. 2)-optimality and minimum discrepancy in 2-level supersaturated designs, Statist. Sin. 12 (2002) 931-939.
11. X. Lu, W. Hu, Y. Zheng, A systematical procedure in the construction of multi-level supersaturated designs, J. Statist. Plann. Inference 15 (2003) 287-310.
12. X. Lu, Y. Sun, Supersaturated designs with more than two levels, Chinese Ann. Math. B 22 (2001) 183-194.
13. P. Winker, Optimization Heuristics in Econometrics: Applications of Threshold Accepting, Wiley, Chichester, 2001.
14. P. Winker, K.-T. Fang, Application of threshold accepting to the evaluation of the discrepancy of a set of points, SIAM J. Numer. Anal. 34 (1997) 2028-2042.
15. P. Winker, K.-T. Fang, Optimal U-type designs, in: H. Niederreiter, P. Hellekalek, G. Larcher, P. Zinterhof (Eds.), Monte Carlo and Quasi-Monte Carlo Methods, Springer, New York, 1997, pp. 436-488.