Mathematics – Statistics Theory
Scientific paper
2007-08-14
Annals of Statistics 2007, Vol. 35, No. 2, 772-792
Mathematics
Statistics Theory
Published at http://dx.doi.org/10.1214/009053606000001307 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053606000001307
We consider maximin and Bayesian $D$-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior for these parameters is available. On interval parameter spaces, it was observed empirically by many authors that an increase of uncertainty in the prior information (i.e., a larger range for the parameter space in the maximin criterion or a larger variance of the prior in the Bayesian criterion) yields a larger number of support points of the corresponding optimal designs. In this paper, we present analytic tools which are used to prove this phenomenon in concrete situations. The proposed methodology can be used to explain many empirically observed results in the literature. Moreover, it explains why maximin $D$-optimal designs are usually supported at more points than Bayesian $D$-optimal designs.
Braess Dietrich
Dette Holger
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