Optimal experimental designs for inverse quadratic regression models

TL;DR

This paper develops optimal experimental designs for inverse quadratic regression models, analyzing different parameterizations and criteria to identify efficient, robust, and geometrically supported designs for parameter estimation.

Contribution

It introduces new optimal design strategies for inverse quadratic models considering multiple criteria and parameterizations, highlighting geometric allocation rules and design efficiencies.

Findings

Geometric allocation rules are optimal for large design spaces.

Designs with different optimality criteria often share support points.

Some commonly used designs are less efficient compared to optimal designs.

Abstract

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.