KL-optimum designs: theoretical properties and practical computation

TL;DR

This paper introduces new theoretical properties and computational methods for finding KL-optimum designs, which are crucial for selecting experimental conditions to effectively discriminate between statistical models.

Contribution

It provides new insights into the properties of KL-optimum designs and develops practical algorithms for their computation, including invariance and convergence results.

Findings

Proved continuity of the KL-optimality criterion.

Established convergence of the first-order algorithm.

Demonstrated invariance of KL-optimum designs to scale-position transformations.

Abstract

In this paper some new properties and computational tools for finding KL-optimum designs are provided. KL-optimality is a general criterion useful to select the best experimental conditions to discriminate between statistical models. A KL-optimum design is obtained from a minimax optimization problem, which is defined on a infinite-dimensional space. In particular, continuity of the KL-optimality criterion is proved under mild conditions; as a consequence, the first-order algorithm converges to the set of KL-optimum designs for a large class of models. It is also shown that KL-optimum designs are invariant to any scale-position transformation. Some examples are given and discussed, together with some practical implications for numerical computation purposes.