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\noindent Statistica Sinica {\bf 17}(2007), 463-480

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\centerline{\large\bf MAXIMIN AND BAYESIAN OPTIMAL DESIGNS}
\vspace{2pt}
\centerline{\large\bf  FOR REGRESSION MODELS}
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\author{Holger Dette, Linda M. Haines and Lorens A. Imhof}
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\centerline{\it Ruhr-Universit\"at, University of Cape Town and Bonn
University}
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\begin{quotation}
\noindent {\it Abstract:}
For many problems of statistical inference in regression modelling,
the Fisher information matrix depends on certain nuisance parameters
which are unknown and which enter the model nonlinearly. A common
strategy to deal with this problem
 is to construct maximin optimal designs,
that  maximize the minimum value of a real-valued (standardized)
function of the Fisher information matrix, where the minimum is
taken over a specified range of the unknown parameters. The maximin
criterion is not differentiable and the construction of the
associated optimal designs is therefore difficult to achieve in
practice. In the present paper the relationship between maximin
optimal designs and a class of Bayesian optimal designs for which
the associated criteria are differentiable is explored. In
particular, a general methodology for determining maximin optimal
designs is introduced based on the fact that in many cases these
designs can be obtained as weak limits of appropriate Bayesian
optimal designs.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Bayesian optimal designs, least favourable prior, maximin optimal
designs, nonlinear regression models, parameter estimation. \par
\end{quotation}

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