On the construction of optimal designs

References

• Smith , K. 1918 . On the standard deviations of adjusted and interpolated of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations . Biometrika , 12 : 1 – 58 .
   Google Scholar
• Guest , P. G. 1958 . The spacing of observations in polynomial regression . Ann. Math. Statist. , 29 : 294 – 299 .
   Google Scholar
• Kiefer , J. and Wolfowitz , J. 1959 . Optimum designs in regression problems . Ann. Math. Statist. , 30 : 271 – 294 .
   Google Scholar
• Song , D. and Wong , W. K. 1999 . On the construction of GRM-optimal designs . Statistica Sinica , 9 : 263 – 272 .
   Web of Science ®Google Scholar
• Wald , A. 1943 . On the efficient design of statistical investigation . Ann. Math. Statist. , 14 : 134 – 140 .
   Google Scholar
• Mood , A. M. 1946 . On hotelling's weighing problem . Ann. Math. Statist. , 17 : 432 – 446 .
   Google Scholar
• Kiefer , J. 1961 . Optimum designs in regression problems, II . Ann. Math. Statist. , 32 ( 1 ) : 298 – 325 .
   Google Scholar
• Wynn , H. P. 1970 . The sequential generation of D-optimum experimental designs . Ann. Math. Statist. , 41 : 1655 – 1664 .
   Google Scholar
• Box , M. J. and Draper , N. R. 1971 . Factorial designs, the criterion, and some related matters . Technometrics , 13 ( 4 ) : 731 – 742 .
   Web of Science ®Google Scholar
• Mitchell , T. J. 2000 . An algorithm for the construction of ‘D-optimal’ experimental designs . Technometrics , 42 ( 1 ) : 48 – 54 .
   Web of Science ®Google Scholar
• Li , K. , Lau , T. and Zhang , C. 2005 . A note on D-optimal designs for models with and without an intercept . Statist. Papers , 46 : 451 – 458 .
   Web of Science ®Google Scholar
• Dey , A. and Mukerjee , R. 2006 . D-optimal designs for covariate models . Statistics , 40 ( 4 ) : 297 – 305 .
   Web of Science ®Google Scholar
• Karlin , S. and Studden , W. J. 1966 . Optimal experimental designs . Ann. Math. Statist. , 37 : 783 – 815 .
   Google Scholar
• Atwood , C. L. 1969 . Optimal and efficient design of experiments . Ann. Math. Statist. , 40 : 1570 – 1602 .
   Google Scholar
• John , R. C. St. and Draper , N. R. 1975 . D-optimality for regression designs: a review . Technometrics , 17 ( 1 ) : 15 – 23 .
   Web of Science ®Google Scholar
• Ehrenfeld , S. 1955 . On the efficiencies of experimental designs . Ann. Math. Statist. , 26 : 247 – 255 .
   Google Scholar
• Kiefer , J. 1958 . On the nonrandomized optimality and randomized nonoptimality of symmetrical designs . Ann. Math. Statist. , 29 : 675 – 699 .
   Google Scholar
• Moerbeek , M. 2005 . Robustness properties of A-, D-, and E-optimal designs for polynomial growth models with autocorrelated errors . Comput. Statist. Data Anal. , 48 ( 4 ) : 765 – 778 .
   Web of Science ®Google Scholar
• Elfving , G. 1952 . Optimum allocation in linear regression Statist theory . Ann. Math. , 23 : 255 – 262 .
   Google Scholar
• Chernoff , H. 1953 . Locally optimum designs for estimating parameters . Ann. Math. Statist. , 24 : 586 – 602 .
   Google Scholar
• Gaylor , D. W. and Merrill , J. A. 1968 . Augmenting existing data in multiple regression . Technometrics , 10 : 73 – 81 .
   Web of Science ®Google Scholar
• Dykstra , O. J. 1966 . The orthogonalization of undesigned experiments . Technometrics , 8 ( 2 ) : 279 – 290 .
   Web of Science ®Google Scholar
• Dykstra , O. Jr . 1971 . The augmentation of experimental data to maximize . Technometrics , 13 ( 3 ) : 682 – 688 .
   Web of Science ®Google Scholar
• Heiberger , R. M. , Bhaumik , D. K. and Holland , B. 1993 . Optimal data augmentation strategies for additive models . J. Amer. Statist. Assoc. , 88 ( 423 ) : 926 – 938 .
   Web of Science ®Google Scholar
• Kiani , M. 2010 . Extensions to modified gram-schmidt strategy and its application in steepest ascent method . J. Statist. Comput. Simul. , 80 ( 4 ) : 389 – 400 .
   Web of Science ®Google Scholar
• Heredia-Laugner , A. , Carlyle , W. M. , Montgomery , D. C. , Borror , C. M. and Runger , G. C. 2003 . Genetic algorithms for the construction of D-optimal designs . J. Qual. Technol. , 35 ( 1 ) : 28 – 46 .
   Web of Science ®Google Scholar
• DeGroot , M. H. and Goel , P. K. 1979 . Bayesian estimation and optimal design in partially accelerated life testing . Naval Res. Logist. Quart. , 26 : 223 – 235 .
   Google Scholar
• Khuri , A. I. , Mukherjee , B. , Sinha , B. K. and Ghosh , M. 2006 . Design issues for generalized linear models: A review . Statist. Sci. , 21 ( 3 ) : 376 – 399 .
   Web of Science ®Google Scholar
• Dror , H. A. and Steinberg , D. M. 2008 . Sequential experimental designs for generalized linear models . J. Amer. Statist. Assoc. , 21 ( 3 ) : 376 – 399 .
   Google Scholar