Efficient maximin distance designs for experiments in mixtures

References

• Aitchison , J. 1986 . “ The Statistical Analysis of Compositional Data ” . London : Chapman & Hall .
   Google Scholar
• Aitchison , J. 1992 . On criteria for measures of compositional difference . Math. Geol. , 24 : 365 – 379 .
   Google Scholar
• Borkowski , J. J. and Piepel , G. F. 2009 . Uniform designs for highly constrained mixture experiments . J. Qual. Technol. , 41 : 35 – 47 .
   Web of Science ®Google Scholar
• Bratley , P. and Fox , B. L. 1988 . Algorithm 659: Implementing Sobol's quasirandom sequence generator . ACM Trans. Math. Softw. , 14 : 88 – 100 .
   Web of Science ®Google Scholar
• Cha , S. H. 2007 . Comprehensive survey on distance/similarity measures between probability density functions . Int. J. Math. Models Methods in Appl. Sci. , 1 : 300 – 307 .
   Google Scholar
• Cook , R. D. and Nachtsheim , C. J. 1980 . A comparison of algorithms for constructing exact d-optimal designs . Technometrics , 22 : 315 – 324 .
   Web of Science ®Google Scholar
• Cox , T. F. and Cox , M. A. 2001 . Multidimensional Scaling , 2 , Boca Raton , FL : Monographs on Statistics and Applied Probability 88, Chapman & Hall/CRC .
   Google Scholar
• Fang , K. T. , Li , R. and Sudjianto , A. 2006 . “ Design and Modeling for Computer Experiments ” . Boca Raton , FL : Computer Science and Data Analysis Series, Chapman & Hall/CRC .
   Google Scholar
• Fedorov , V. V. 1972 . “ Theorey of Optimal Experiments ” . New York : Academic Press .
   Google Scholar
• Galil , Z. and Kiefer , J. 1980 . Time- and space-saving computer methods, related to Mitchell's DETMAX, for finding d-optimum designs . Technometrics , 22 : 301 – 313 .
   Web of Science ®Google Scholar
• Gower , J. C. 1982 . Euclidean distance geometry . Math. Sci. , 7 : 1 – 14 .
   Google Scholar
• Gower , J. C. and Legendre , P. 1986 . Metric and Euclidean properties of dissimilarity coefficients . J. Classification , 3 : 5 – 48 .
   Web of Science ®Google Scholar
• Haines , L. M. 1987 . The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models . Technometrics , 29 : 439 – 447 .
   Web of Science ®Google Scholar
• Johnson , M. E. , Moore , L. M. and Ylvisaker , D. 1990 . Minimax and maximin distance designs . J. Stat. Plann. Inference , 26 : 131 – 148 .
   Web of Science ®Google Scholar
• Jourdan , A. and Franco , J. “ A new criterion based on Kullback-Leibler information for space-filling designs ” . Preprint (2009). Available at http://adsabs.harvard.edu/abs/2009arXiv0904.2456J.
   Google Scholar
• Miller , A. J. and Nguyen , N. 1994 . Algorithm as 295: A Fedorov exchange algorithm for d-optimal design . Appl. Stat. , 43 : 669 – 677 .
   Web of Science ®Google Scholar
• Mitchell , T. J. 1974 . An algorithm for the construction of “d-optimal” experimental designs . Technometrics , 16 : 203 – 210 .
   Web of Science ®Google Scholar
• Mitchell , T. J. 1974 . Computer construction of “d-optimal” first-order designs . Technometrics , 16 : 211 – 220 .
   Web of Science ®Google Scholar
• Naryanan , A. 1991 . Algorithm as 266: Maximum likelihood estimation of the parameters of the dirichlet distribution . Appl. Stat. , 40 : 365 – 374 .
   Web of Science ®Google Scholar
• Piepel , G. F. 1988 . Programs for generating extreme vertices and centroids of linear constrained experimental regions . J. Qual. Technol. , 20 : 125 – 139 .
   Web of Science ®Google Scholar
• Sacks , J. , Welch , W. J. , Mitchell , T. J. and Wynn , H. P. 1989 . Design and analysis of computer experiments . Stat. Sci. , 4 : 409 – 423 .
   Google Scholar
• Santner , T. J. , Williams , B. J. and Notz , W. I. 2003 . “ The Design and Analysis of Computer Experiments ” . Springer Series in Statistics New York : Springer-Verlag .
   Google Scholar
• Shewry , M. C. and Wynn , H. P. 1987 . Maximum entropy sampling . J. Appl. Stat. , 14 : 165 – 170 .
   Google Scholar
• Snee , R. D. 1979 . Experimental designs for mixture systems with multicomponent constraints . Comm. Statist. Theory Methods A , 8 : 303 – 326 .
   Web of Science ®Google Scholar
• Snee , R. D. and Marquardt , D. W. 1974 . Extreme vertices designs for linear mixture models . Technometrics , 16 : 399 – 408 .
   Web of Science ®Google Scholar
• Stat-Ease, Design-Expert, Version 6.0.6. Stat-Ease, Inc., Minneapolis, MN, 2002. Available at http://www.statease.com.
   Google Scholar
• Stinstra , E. , Stehouwer , P. , Hertogden , D. and Vestjens , A. 2003 . Constrained maximin designs for computer experiments . Technometrics , 45 : 340 – 346 .
   Web of Science ®Google Scholar
• Welch , W. J. 1982 . Branch-and-bound search for experimental designs based on d optimality and other criteria . Technometrics , 24 : 41 – 48 .
   Web of Science ®Google Scholar
• Welch , W. J. 1984 . Computer-aided design of experiments for response estimation . Technometrics , 26 : 217 – 224 .
   Web of Science ®Google Scholar