Local mixture models of exponential families

TL;DR

This paper introduces local mixture models for exponential families, enhancing their flexibility while preserving key inferential properties like identifiability and log-concavity.

Contribution

It develops a novel local mixture modeling approach for exponential families, maintaining interpretability and inferential advantages.

Findings

Models retain interpretability and flexibility.

Key properties like identifiability are preserved.

Likelihood remains log-concave under the new models.

Abstract

Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which this set of tools can be enriched in a natural and interpretable way is through mixing. This paper develops and applies the idea of local mixture modelling to exponential families. It shows that the highly interpretable and flexible models which result have enough structure to retain the attractive inferential properties of exponential families. In particular, results on identification, parameter orthogonality and log-concavity of the likelihood are proved.