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REGRESSION ANALYSIS

The Mean Squared Error Optimum Design Criterion for Parameter Estimation in Nonlinear Regression Models

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Pages 508-519 | Received 13 Oct 2006, Accepted 11 May 2007, Published online: 13 Feb 2008

References

  • Atkinson , A. C. ( 1982 ). Developments in the design of experiments . Rev. Int. Statist. Inst. 50 : 161 – 177 .
  • Atkinson , A. C. ( 1996 ). The usefulness of optimum experimental designs (with discussion) . J. R. Statist. Soc. B 58 : 59 – 76 .
  • Atkinson , A. C. ( 2003 ). Horwitz's rule, transforming both sides and the design of experiments for mechanistic models . Appl. Statist. 52 : 261 – 278 .
  • Atkinson , A. C. ( 2005 ). Robust optimum designs for transformation of the responses in a multivariate chemical kinetic model . Technometrics 47 : 478 – 487 .
  • Atkinson , A. C. , Hunter , W. G. ( 1968 ). The design of experiments for parameter estimation . Technometrics 10 : 271 – 289 .
  • Atkinson , A. C. , Donev , A. N. ( 1992 ). Optimum Experimental Designs . London : Oxford University Press .
  • Atkinson , A. C. , Bailey , R. A. ( 2001 ). One hundred years of the design of experiments on and off the pages of Biometrika . Biometrika 88 : 53 – 97 .
  • Bates , D. M. , Watts , D. G. ( 1980 ). Relative curvature measures of nonlinearity (with discussion) . J. R. Statist. Soc. B 42 : 1 – 25 .
  • Bates , D. M. , Watts , D. G. ( 1981 ). Parameter transformations for improved approximate confidence regions in nonlinear least squares . Ann. Statist. 9 : 1152 – 1167 .
  • Bates , D. M. , Watts , D. G. ( 1988 ). Nonlinear Regression: Analysis and Its Applications . New York : Wiley .
  • Bates , D. M. , Hamilton , D. C. , Watts , D. G. ( 1983 ). Calculation of intrinsic and parameter-effects curvatures for nonlinear regression models . Commun. Statist. Theor. Meth. 12 : 469 – 477 .
  • Box , M. J. ( 1968 ). The occurrence of replications in optimal designs of experiments to estimate parameters in non-linear models . J. R. Statist. Soc. B 30 : 290 – 302 .
  • Box , M. J. ( 1970 ). Some experiences with a nonlinear experimental design criterion . Technometrics 12 : 569 – 589 .
  • Box , M. J. ( 1971 ). Bias in nonlinear estimation (with discussion) . J. R. Statist. Soc. B 33 : 171 – 201 .
  • Box , G. E. P. , Lucas , H. L. ( 1959 ). Design of experiments in non-linear situations . Biometrika 46 : 77 – 90 .
  • Chaudhuri , P. , Mykland , P. A. (1993). Nonlinear experiments: Optimal design and inference based on likelihood. J. Am. Statist. Assoc. 88:538–546.
  • Chernoff , H. ( 1953 ). Locally optimal designs for estimating parameters . Ann. Math. Statist. 24 : 586 – 602 .
  • Clarke , G. P. Y. ( 1980 ). Moments of the least squares estimators in a non-linear regression model . J. R. Statist. Soc. B 42 : 227 – 237 .
  • Cochran , W. G. ( 1973 ). Experiments for nonlinear functions . J. Am. Statist. Assoc. 44 : 32 – 61 .
  • Daimon , T. , Goto , M. ( 2003 ). Optimum design of sampling times for inference of compartment models . J. Jpn. Soc. Comp. Stat. 16 : 23 – 38 .
  • Dette , H. , Biedermann , S. ( 2003 ). Robust and efficient design for the Michaelis–Menten model . J. Am. Statist. Assoc. 98 : 679 – 686 .
  • Dette , H. , Melas , V. , Pepelyshev , A. , Strigul , N. ( 2003 ). Efficient design of experiments in the Monod model . J. R. Statist. Soc. B 65 : 725 – 742 .
  • Dette , H. , Melas , V. , Pepelyshev , A. ( 2004 ). Optimal designs for a class of nonlinear regression models . Ann. Statist. 32 : 2142 – 2167 .
  • Dette , H. , Melas , V. , Wong , W. K. ( 2005 ). Optimal design for goodness-of-fit of the Michaelis–Menten enzyme kinetic function . J. Am. Statist. Assoc. 100 : 1370 – 1381 .
  • Ford , I. , Titterington , D. M. , Kitsos , C. P. ( 1989 ). Recent advances in nonlinear experimental design . Technometrics 31 : 49 – 60 .
  • Hamilton , D. C. , Watts , D. G. ( 1985 ). A quadratic design criterion for precise estimation in nonlinear regression models . Technometrics 27 : 241 – 250 .
  • Han , C. , Chaloner , K. ( 2004 ). Bayesian experimental design for nonlinear mixed-effects models with application to HIV dynamics . Biometrics 60 : 25 – 33 .
  • Hougaard , P. ( 1985 ). The appropriateness of the asymptotic distribution in a nonlinear regression model in relation to curvature . J. R. Statist. Soc. B 47 : 103 – 114 .
  • Hughes-Oliver , J. M. ( 1998 ). Optimal designs for nonlinear models with correlated errors . In: Flournoy , N. , Rosenberger , W. F. , Wong , W. K. , eds. New Developments and Applications in Experimental Design . Institute of Mathematical Statistics. Lecture Notes—Monograph Series No. 34, Hayward, California , pp. 163 – 174 .
  • Melas , V. B. ( 2006 ). Functional Approach to Optimal Experimental Design (Lecture Notes in Statistics) . New York : Springer .
  • Mentré , F. , Mallet , A. , Baccar , D. ( 1997 ). Optimal design in random-effects regression models . Biometrika 84 : 429 – 442 .
  • Mukhopadhyay , S. , Haines , L. M. ( 1995 ). Bayesian D-optimal designs for the exponential growth model . J. Statist. Planng. Inf. 44 : 385 – 397 .
  • Müller , W. G. , Pázman , A. ( 2003 ). Measures for designs in experiments with correlated errors . Biometrika 84 : 429 – 442 .
  • O'Brien , T. E. ( 1992 ). A note on quadratic designs for nonlinear regression models . Biometrika 79 : 847 – 849 .
  • Seber , G. A. F. , Wild , C. J. ( 1989 ). Nonlinear Regression . New York : Wiley .
  • Silvey , S. D. ( 1980 ). Optimum Design . London : Chapman and Hall .
  • St. John , R. C. , Draper , N. R. ( 1975 ). D-optimality for regression designs: a review . Technometrics 17 : 15 – 23 .
  • Uciński , D. , Bogacka , B. ( 2005 ). T-optimum designs for discrimination between two multiresponse dynamic models . J. R. Statist. Soc. B 67 : 3 – 18 .

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