Discrete discrepancy in factorial designs

Metrika

Volumn 60, Issue 1, 2004, Pages 59-72

  Qin, Hong ^a,b   Fang, Kai Tai ^b  

^a CENTRAL CHINA NORMAL UNIVERSITY   (China)

^b HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Discrete discrepancy; Factorial design; Generalized minimum aberration; Minimum moment aberration; Uniformity

Indexed keywords

EID: 17444408830     PISSN: 00261335     EISSN: None     Source Type: Journal    
DOI: 10.1007/s001840300296     Document Type: Article

References (27)

1. Booth KHV, Cox DR (1962) Some systematic supersaturated designs. Technometrics 4:489-495
2. Fang KT (2002) Some applications of Quasi-Monte Carlo methods in statistics. In: Fang KT, Hickernell FJ, Niederreiter H (eds) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Springer-Verlag, Berlin
3. Fang KT, Lin DKJ, Winker P, Zhang Y (2000) Uniform design: theory and applications. Technometrics 42:237-248
4. s-1. In: Fang KT, Hickernell FJ, Niederreiter H (eds) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Springer-Verlag, Berlin
5. Fang KT, Ma CX, Mukerjee R (2002) Uniformity in fractional factorials. In: Fang KT, Hickernell FJ, Niederreiter H (eds) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Springer-Verlag, Berlin
6. Fang KT, Mukerjee R (2000) A connection between uniformity and aberration in regular fractions of two-level factorials. Biometrika 87:173-198
7. Fang KT, Wang Y (1994) Number-Theoretic Methods in Statistics. London: Chapman and Hall
8. n-m designs. Technometrics 26:225-232
9. k-p designs. Technometrics 22:601-608
10. Hickernell FJ (1998a) A generalized discrepancy and quadrature error bound. Math Comp 67:299-322
11. Hickernell FJ (1998b) Lattice Rules: How Well Do They Measure Up? In: Hellekalek P, Larcher G (eds) Random and Quasi-Random Point Sets. Lecture Notes in Statistics Vol. 138:109-166, New York: Springer
12. Hickernell FJ (2000) What affects the accuracy of quasi-Monte Carlo quadrature? In: Niederreiter H, Spanier J (eds) Monte Carlo and Quasi-Monte Carlo Methods 1998. 16-55. Berlin: Springer-Verlag
13. Hickernell FJ, Liu MQ (2002) Uniform designs limit aliasing. Biometrika 89:893-904
14. Lin DKJ, Draper NR (1992) Projection properties of Plackett and Burman designs. Technometrics 34:423-428
15. Liu MQ (2002) Using discrepancy to evaluate fractional factorial designs. In: Fang KT, Hickernell FJ, Niederreiter H (eds) Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Springer-Verlag, Berlin
16. 2)-optimality and minimum discrepancy in 2-level supersaturated designs. Statist Sinica 12:931-939
17. Ma CX, Fang KT (2001) A note on generalized aberration factorial designs. Metrika 53:85-93
18. Ma CX, Fang KT, Lin DKJ (2003) A note on uniformity and orthogonality. J Statist Planning and Inference 113:323-334
19. MacWilliams FJ, Sloane NJA (1977) The theory of error-correcting codes. North-Holland, Amsterdam
20. Marshall AW, Olkin I (1979) Inequalities: Theory of Majorization and its Applications. New York: Academic Press
21. Sloane NJA, Stufken J (1996) A linear programming bound for orthogonal arrays with mixed levels. J Statist Planning and Inference 56:295-305
22. 2-aberration for nonregular fractional designs. Ann Statist 27:1914-1926
23. Wang Y, Fang KT (1981) A note on uniform distribution and experimental design. Chin Sci Bull 26:485-489
24. Weyl H (1916) Über die Gleichverteilung der Zahlen mod eins. Math Ann 77:313-352
25. Xu H (1999) Universally optimal designs for computer experiments. Statistica Sinica 9:1083-1088
26. Xu H (2003) Minimum moment aberration for nonregular designs and supersaturated designs. Statistica Sinica 13:691-708
27. Xu H, Wu CFJ (2001) Generalized minimum aberration for asymmetrical fractional factorial designs. Ann Statist 29:549-560