Optimal discrimination designs for semi-parametric models

TL;DR

This paper develops a practical approach for finding optimal discrimination designs among semi-parametric models, extending existing criteria and providing theoretical insights and verification methods.

Contribution

It introduces a new strategy for semi-parametric discrimination design optimization, generalizes the KL-optimality criterion, and links to T-optimal designs.

Findings

Proposes a practical method for semi-parametric discrimination design optimization.

Provides an equivalence theorem for verification of optimality.

Identifies cases where semi-parametric designs coincide with T-optimal designs.

Abstract

Much of the work in the literature on optimal discrimination designs assumes that the models of interest are fully specified, apart from unknown parameters in some models. Recent work allows errors in the models to be non-normally distributed but still requires the specification of the mean structures. This research is motivated by the interesting work of Otsu (2008) to discriminate among semi-parametric models by generalizing the KL-optimality criterion proposed by L\'opez-Fidalgo et al. (2007) and Tommasi and L\'opez-Fidalgo (2010). In our work we provide further important insights in this interesting optimality criterion. In particular, we propose a practical strategy for finding optimal discrimination designs among semi-parametric models that can also be verified using an equivalence theorem. In addition, we study properties of such optimal designs and identify important cases where the proposed semi-parametric optimal discrimination designs coincide with the celebrated T -optimal designs.