Abstract
An overview is given of the link between the k-circulant method of construction of two-level supersaturated designs and construction methods based on cyclic incomplete block designs. It is shown that this link enables a simple formula for the Es2-efficiency of all such designs to be derived. Generators are given for Es2-optimal and near-optimal designs that extend the range of previously known designs or that have a smaller number of highly correlated column pairs.
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Abraham, B., Chipman, H., Vijayan K., 1999. Some risks in the construction and analysis of supersaturated designs. Technometrics, 41 (2), 135–141.
Beattie, S.D., Fong, D.K.H., Lin, D.K.J., 2002. A two-stage Bayesian model selection strategy for supersaturated designs. Technometrics, 22 (1), 55–63.
Booth, K.H.V., Cox, D.R., 1962. Some systematic supersaturated designs. Technometrics, 4, 489–495.
Box, G.E.P., Meyer, R.D., 1986. An analysis for unreplicated fractional factorials. Technometrics, 28, 11–18.
Bulutoglu, D.A., Cheng, C.S., 2004. Construction of E(s2)-optimal supersaturated designs. Annals of Statistics, 32, 1662–1678.
Butler, N.A., Mead, R., Eskridge, K.M., Gilmour, S.G., 2001. A general method of constructing E(s2)-optimal supersaturated designs. J. R. Statist. Soc., B, 63, 621–632.
Chen, J., Lin, D.K.J., 1998. On the identifiability of a supersaturated design. Journal of Statistical Planning and Inference, 72, 99–107.
Cheng, C.S., 1997. E(s2)-optimal supersaturated designs. Statistica Sinica, 7, 929–939.
Chipman, H., Hamada, M., Wu, C.F.J., 1997. A Bayesian variable-selection approach for analyzing designed experiments with complex aliasing. Technometrics, 39, 372–381.
Das, A., Dey, A., Chan, L., Chatterjee, K. (2008). On E(s2)-optimal supersaturated designs. Journal of Statistical Planning and Inference, 138, 3746–3757.
Eskridge, K.M., Gilmour, S.G., Mead, R., Butler, N.A., Travnicek, D.A., 2004. Large supersaturated designs. J. Stat. Comput. Simul., 74, 525–542.
Georgiou, S.D., 2008. On the construction of E(s2)-optimal supersaturated designs, Metrika, 68, 189–198.
Geramita, A.V., Seberry, J., 1979. Orthogonal Designs: Quadratic forms and Hadamard Matrices. Marcel Dekker, New York-Basel.
Kelly, H.W., III, Voelkel, J.O., 2000. Asymptotic-power problems in the analysis of supersaturated designs. Statistics and Probability Letters, 47, 317–324.
Li, R., Lin, D.K.J., 2003. Analysis methods for supersaturated design: Some comparisons. Journal of Data Science, 1, 249–260.
Li, W., Wu, C.F.J., 1997. Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics, 39, 171–179.
Lin, D.K.J., 1993. A new class of supersaturated designs. Technometrics, 35, 28–31.
Lin, D.K.J., 1995. Generating systematic supersaturated designs. Technometrics, 37, 213–225.
Liu, Y., Dean, A.M., 2004. k-circulant supersaturated designs. Technometrics, 46, 32–43.
Liu, Y., Ruan, S., Dean, A.M., 2006. Construction and analysis of Es2 efficient supersaturated designs. Journal of Statistical Planning and Inference, 137, 1516–1529.
Liu, M., Zhang, R., 2000. Construction of E(s2) optimal supersaturated designs using cyclic BIBDs. Journal of Statistical Planning and Inference, 91, 139–150.
Meyer, R.D., Wilkinson, R.G., 1998. Bayesian variable assessment. Communications in Statistics: Theory and Methods, 27, 2675–2705.
Nguyen, N.K., 1996. An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.
Phoa, F., Pan, Y.-H., Xu, H., 2009. Analysis of Supersaturated Designs via Dantzig Selector. Journal of Statical Planning and Inference, 7, 2362–2372.
Plackett, R.L., Burman, J.P., 1946. The design of optimum multifactorial experiments. Biometrika, 33, 305–325.
Satterthwaite, F.E., 1959. Random balance experimentation (with discussions). Technometrics, 1, 111–137.
Ryan, K.J., Bulutoglu, D.A., 2007. Es2-optimal supersaturated designs with good minimax properties. Journal of Statistical Planning and Inference, 137, 2250–2262.
Street, A.P., Street, D.J., 1987. Combinatorics of Experimental Design. Oxford Science Publications.
Tang, B., Wu, C.F.J., 1997. A method for constructing supersaturated designs and its Es2 optimality. Canadian Journal of Statistics, 25, 191–201.
Wallis, W.D., Street, A.P., Seberry, J. Wallis, 1972. Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices. Lecture Notes in Mathematics, Vol. 292, Springer-Verlag, Berlin, Heidelberg, New York.
Westfall, P.H., Young, S.S., Lin, D.K.J., 1998. Forward selection error control in the analysis of supersaturated designs. Statistica Sinica, 8, 101–117.
Wu, C.F.J., 1993. Construction of supersaturated designs through partially aliased interactions. Biometrika, 80, 661–669.
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Georgiou, S.D., Draguljić, D. & Dean, A.M. An Overview of Two-level Supersaturated Designs with Cyclic Structure. J Stat Theory Pract 3, 489–504 (2009). https://doi.org/10.1080/15598608.2009.10411940
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DOI: https://doi.org/10.1080/15598608.2009.10411940