Optimal discrimination designs

TL;DR

This paper studies the construction and properties of optimal designs for discriminating between competing regression models, providing explicit solutions and characterizations for $T$-optimal designs, and comparing them with alternative criteria through simulations.

Contribution

It introduces new properties of $T$-optimal designs, offers explicit determination methods, and characterizes all $T$-optimal designs in certain cases, advancing the theory of optimal discrimination designs.

Findings

Explicit determination of $T$-optimal designs in many cases.

Characterization of all $T$-optimal designs when non-uniqueness occurs.

Comparison of $T$-optimal designs with alternative criteria via simulation.

Abstract

We consider the problem of constructing optimal designs for model discrimination between competing regression models. Various new properties of optimal designs with respect to the popular $T$-optimality criterion are derived, which in many circumstances allow an explicit determination of $T$-optimal designs. It is also demonstrated, that in nested linear models the number of support points of $T$-optimal designs is usually too small to estimate all parameters in the extended model. In many cases $T$-optimal designs are usually not unique, and in this situation we give a characterization of all $T$-optimal designs. Finally, $T$-optimal designs are compared with optimal discriminating designs with respect to alternative criteria by means of a small simulation study.