D-optimum designs for heteroscedastic linear models

R. D. Cook, A. C. Atkinson

Research output: Contribution to journalArticle

41 Scopus citations


The methods of optimum experimental design are applied to models in which the variance, as well as the mean, is a parametric function of explanatory variables. Extensions to standard optimality theory lead to designs when the parameters of both the mean and the variance functions, or the parameters of only one function, are of interest. The theory also applies whether the mean and variance are functions of the same variables or of different variables, although the mathematical foundations differ. The example studied is a second-order two-factor response surface for the mean with a parametric nonlinear variance function. The theory is used both for constructing designs and for checking optimality. A major potential for application is to experimental design in off-line quality control.

Original languageEnglish (US)
Pages (from-to)204-212
Number of pages9
JournalJournal of the American Statistical Association
Issue number429
StatePublished - Mar 1995


  • Bayesian design
  • General equivalence theorem
  • Taguchi methods

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