KL-optimum designs: theoretical properties and practical computation

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 scaleposition transformation. Some examples are given and discussed, together with some practical implications for numerical computation purposes. Keywords Optimum design · KL-optimality · Discrimination · Infinite-dimensional spaces · Continuity · Weak convergence metric · Convexity · Invariance · Regular designs · Generalized linear models Mathematics Subject Classification 62K05 · 62-0