Invariance and Equivariance in Experimental Design for Nonlinear Models

  • Martin RadloffEmail author
  • Rainer Schwabe
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


In this note we exhibit the usefulness of invariance considerations in experimental design in the context of nonlinear models. Therefor we examine the equivariance of locally optimal designs and their criteria functions and establish the optimality of invariant designs with respect to robust criteria like weighted or maximin optimality, which avoid parameter dependence.


Optimal Design Prior Distribution Information Matrix Linear Predictor Design Region 
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  1. 1.
    Atkinson, A.C., Donev, A.N., Tobias, R.D.: Optimum Experimental Designs, with SAS. Oxford University Press, Oxford (2007)zbMATHGoogle Scholar
  2. 2.
    Firth, D., Hinde, J.: On Bayesian D-optimum design criteria and the equivalence theorem in non-linear Models. J. R. Stat. Soc. Ser. B Methodol. 59, 793–797 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Ford, I., Torsney, B., Wu, C.F.J.: The use of a canonical form in the construction of locally optimal designs for non-linear problems. J. R. Stat. Soc. Ser. B Methodol. 54, 569–583 (1992)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Gaffke, N., Heiligers, B.: Approximate designs for polynomial regression: invariance, admissibility, and optimality. In: Ghosh, S., Rao, C.R. (eds.) Handbook of Statistics, vol. 13, pp. 1149–1199. Elsevier, Amsterdam (1996)Google Scholar
  5. 5.
    Graßhoff, U., Schwabe, R.: Optimal designs for the Bradley-Terry paired comparison model. Stat. Methods Appl. 17, 275–289 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    McCulloch, C.E., Searle, S.R.: Generalized, Linear, and Mixed Models. Wiley, New York (2001)zbMATHGoogle Scholar
  7. 7.
    Pukelsheim, F.: Optimal Design of Experiments. Wiley-Interscience, New York (1993)zbMATHGoogle Scholar
  8. 8.
    Russell, K.G., Woods, D.C., Lewis, S.M., Eccleston, J.A.: D-optimal designs for Poisson regression models. Stat. Sin. 19, 721–730 (2009)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Schmidt, D., Schwabe, R.: On optimal designs for censored data. Metrika 78, 237–257 (2015)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Schwabe, R.: Optimum Designs for Multi-Factor Models. Springer, New York (1996)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute for Mathematical StochasticsOtto-von-Guericke-UniversityMagdeburgGermany

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