Advertisement

Journal of the Italian Statistical Society

, Volume 1, Issue 2, pp 183–202 | Cite as

Optimal designs for generalized linear models

  • J. Burridge
  • P. Sebastiani
Article

Summary

This paper solves some D-optimal design problems for certain Generalized Linear Models where the mean depends on two parameters and two explanatory variables. In all of the cases considered the support point of the optimal designs are found to be independent of the unknown parameters. While in some cases the optimal design measures are given by two points with equal weights, in others the support is given by three point with weights depending on the unknown parameters, hence the designs are locally optimal in general. Empirical results on the efficiency of the locally optimal designs are also given. Some of the designs found can also be used for planning D-optimal experiments for the normal linear model, where the mean must be positive.

Keywords

D-optimality duality theory Generalized Linear Models locally optimal designs 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Atkinson A. C. (1991), Optimum Design of Experiments. InStatistical Theory and Modelling in Honour of Sir David Cox Chapman and Hall: London.Google Scholar
  2. Ford I., Kitsos P. C. andTitterington D. M. (1989), Recent Advances in Nonlinear Experimental Design.Technometrics, 431, 49–60.CrossRefMathSciNetGoogle Scholar
  3. Ford I., Tornsey B. andWu C. F. J. (1991), The Use of a Canonical Form in the Construction of Locally Optimal Designs for Non-linear Problems. Submitted toJ. R. Statist. Soc. B. Google Scholar
  4. Jorgensen B. (1987), Exponential Dispersion Models (with discussion).J. R. Statist. Soc. B, 49, 127–162.MathSciNetGoogle Scholar
  5. Kiefer J. andWolfowitz J. (1960), The equivalence of two extremum problems.Can. J. Math., 412, 363–366.MathSciNetGoogle Scholar
  6. McCullagh P. andNelder J. A. (1989),Generalized Linear Models (second edition). Chapman and Hall: London.zbMATHGoogle Scholar
  7. Rockafellar R. T. (1970),Convex Analysis. Princeton University Press.Google Scholar
  8. Sibson R. (1972), Contribution to Discussion of «Results in the Theory and Construction of D-optimum Experimental Designs» by H. P. Wynn.J. R. Statist. Soc. B, 434, 181–183.Google Scholar
  9. Silvey S. D. andTitterington D. M. (1973), A Geometric Approach to Optimal Design Theory.Biometrika, 460, 21–32.CrossRefMathSciNetGoogle Scholar
  10. Silvey S. D. (1980),Optimal Design. Chapman and Hall: London.zbMATHGoogle Scholar

Copyright information

© Societa Italiana di Statistica 1992

Authors and Affiliations

  • J. Burridge
    • 1
  • P. Sebastiani
    • 2
  1. 1.Dept. Statistical ScienceUniversity College of LondonLondonEngland
  2. 2.Dip. Scienze StatisticheUniversità di PerugiaPerugiaItaly

Personalised recommendations