A two-stage strategy for the construction of d-optimal experimental designs

References

• Atkinson , A.C. and Donev , A.N. 1992 . Optimal Experimental Designs , Oxford : Clarendon Press .
   Google Scholar
• Atkinson , A.C. and Fedorov , V.V. 1975 . The Design of Experiments for Discriminating Between Two Rival Models . Biometrika , 62 : 57 – 60 .
   Web of Science ®Google Scholar
• Benda , N. 1996 . Pre–Test Estimation and Design in the Linear Model . Journal of Statistical Planning and Inference , 52 : 225 – 240 .
   Web of Science ®Google Scholar
• Borth , D. 1975 . A Total Entropy Criterion for the Dual Problem of Model Discrimination and Parameter Estimation . Journal of the Royal Statistical Society B , 37 : 78 – 87 .
   Google Scholar
• Box , G.E.P. and Draper , N.R. 1959 . A Basis for the Selection of A Response Surface Design . Journal of the American Statistical Association , 54 : 622 – 654 .
   Web of Science ®Google Scholar
• Chernoff , H. 1975 . “ Approaches in Sequential Design of Experiments ” . In A Survey of Statistical Design and Linear Models Edited by: Srivastava , J. N. 67 – 90 . New York, , North-Holland
   Google Scholar
• Cook , R.D. and Nachtsheim , C.J. 1982 . Model Robust, Linear-Optimal Designs . Technometrics , 24 : 49 – 54 .
   Web of Science ®Google Scholar
• Dette , H. 1990 . A Generalization of D- and D1Optimal Designs in Polynomial Regression . The Annals of Statistics , 18 : 1784 – 1804 .
   Web of Science ®Google Scholar
• Dette , H. 1992 . Optimal Designs for A Class of Polynomials of Odd or Even Degree . The Annals of Statistics , 20 : 238 – 259 .
   Web of Science ®Google Scholar
• Dette , H. 1993 . On A Mixture of the D- and D1-Optimality Criterion in Polynomial Regression . Journal of Statistical Planning and Inference , 35 : 233 – 249 .
   Web of Science ®Google Scholar
• Dette , H. 1994a . Robust Designs for Multivariate Polynomial Regression on the d cube . Journal of Statistical Planning and Inference , 38 : 105 – 124 .
   Web of Science ®Google Scholar
• Dette , H. 1994b . Discrimination Designs for Polynomial Regression on Compact Intervals . The Annals of Statistics , 22 : 890 – 903 .
   Web of Science ®Google Scholar
• Dette , H. 1995 . Optimal Designs for Identifying the Degree of A Polynomial Regression . The Annals of Statistics , 23 : 1248 – 1266 .
   Web of Science ®Google Scholar
• Dette , H. and Studden , W.J. 1995 . Optimal Designs for Polynomial Regression When the Degree Is Not Known . Statistica Sinica , 5 : 459 – 473 .
   Web of Science ®Google Scholar
• Fedorov , V.V. 1972 . Theory of Optimal Experiments , New York : Academic Press .
   Google Scholar
• Ford , I. , Kitsos , C.P. and Titterington , D.M. 1989 . Recent Advances in Nonlinear Experimental Designs . Technometrics , 31 : 49 – 60 .
   Web of Science ®Google Scholar
• Hill , W. , Hunter , W. and Wichern , D. 1968 . A Joint Design Criterion for the Dual Problem of Model Discrimination and Parameter Estimation . Technometrics , 10 : 145 – 160 .
   Web of Science ®Google Scholar
• Kiefer , J.C. and Wolfowitz , J. 1959 . Optimum Designs in Regression Problems . The Annals of Mathematical Statistics , 30 : 271 – 294 .
   Google Scholar
• Laüter , E. 1974 . Experimental Design in A Class of Models . Mathematische Operations Forschung und Statistik , 5 : 379 – 398 .
   Google Scholar
• Lee , C. M.‐S. 1987 . Constrained Optimal Designs for Regression Models . Communications in Statistics: Theory and Methods , 16 : 765 – 783 .
   Web of Science ®Google Scholar
• Lee , C. M.‐S. 1988 . Constrained Optimal Designs . Journal of Statistical Planning and Inference , 18 : 377 – 389 .
   Web of Science ®Google Scholar
• Li , K.C. and Notz , W. 1982 . Robust Designs for Nearly Linear Regression . Journal of Statistical Planning and Inference , 6 : 135 – 151 .
   Web of Science ®Google Scholar
• Pesotchinsky , L. 1982 . Optimal Robust Designs: Linear Regression in Rk . The Annals of Statistics , 10 : 511 – 525 .
   Web of Science ®Google Scholar
• Pukelsheirn , F. and Rosenberger , J.L. 1993 . Experimental Designs for Model Discriminations . Journal of the American Statistical Association , 88 : 642 – 649 .
   Google Scholar
• Sitter , R.R. and Wu , C.F.J. 1955 . Two-stage Design of Quanta1 Response Studies , Michigan : Department of Statistics, University of Michigan . Technical Report #247, Ann Arbor
   Google Scholar
• Stigler , S.M. 1971 . Optimal Experimental Design for Polynomial Regression . Journal of the American Statistical Association , 66 : 311 – 318 .
   Web of Science ®Google Scholar
• Studden , W.J. 1982 . Some Robust Type D-Optimal Designs in Poly-nomial Regression . Journal of the American Statistical Association , 77 : 916 – 921 .
   Web of Science ®Google Scholar
• Toman , B. 1996 . Bayesian Experimental Design for Multiple Hypothesis Testing . Journal of the American Statistical Association , 91 : 185 – 190 .
   Google Scholar
• Wiens , D.P. 1992 . Minimax Designs for Approximately Linear Regression . Journal of Statistical Planning and Inference , 31 : 353 – 371 .
   Web of Science ®Google Scholar
• Wiens , D. P. 1993 . Designs for Approximately Linear Regression: Maximizing the Minimum Coverage Probability of Confidence Ellipsoids . The Canadian Journal of Statistics , 21 : 59 – 70 .
   Google Scholar