Optimum design via I-divergence for stable estimation in generalized regression models

TL;DR

This paper extends optimal design methods for generalized regression models by using I-divergence to address issues of stability and identifiability in finite samples, especially for models based on exponential families.

Contribution

It introduces a design methodology based on I-divergence for generalized models, improving finite-sample stability and addressing identifiability issues.

Findings

Develops a new design approach using I-divergence.

Applicable to models with exponential family distributions.

Enhances stability and identifiability in finite samples.

Abstract

Optimum designs for parameter estimation in generalized regression models are standardly based on the Fisher information matrix (cf. Atkinson et al (2014) for a recent exposition). The corresponding optimality criteria are related to the asymptotic properties of maximal likelihood (ML) estimators in such models. However, in finite sample experiments there could be problems with identifiability, stability and uniqueness of the ML estimate, which are not reflected by the information matrices. In P\'azman and Pronzato (2014) is discussed how to solve some of these estimability issues on the design stage of an experiment in standard nonlinear regression. Here we want to extend this design methodology to more general models based on exponential families of distributions (binomial, Poisson, normal with parametrized variances, etc.). The main tool for that is the information (or Kullback-Leibler) divergence, which is closely related to the ML estimation.