Optimal experimental designs for inverse quadratic regression models

In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the $c$-, $D$- and $E$-criteria, which reflect various aspects of the precision of the maximum likelihood estimator for the parameters in inverse quadratic regression models. In particular it is demonstrated that for a sufficiently large design space geometric allocation rules are optimal with respect to many optimality criteria. Moreover, in numerous cases the designs with respect to the different criteria are supported at the same points. Finally, the efficiencies of different optimal designs with respect to various optimality criteria are studied, and the efficiency of some commonly used designs are investigated.

💡 Research Summary

The paper addresses the problem of constructing optimal experimental designs for inverse quadratic regression models, a class of nonlinear models frequently encountered in chemistry, biology, and engineering where the response is expressed as the reciprocal of a quadratic function of the predictor. Two distinct parameterizations of the model are considered. The first uses the original coefficients $(\beta_0,\beta_1,\beta_2)$ in the formulation
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