On minimum Bregman divergence inference

TL;DR

This paper introduces a new family of minimum divergence estimators based on Bregman divergence, specifically the exponentially weighted divergence (EWD), and compares its performance with existing estimators through simulations and real data applications.

Contribution

It proposes the exponentially weighted divergence (EWD) as a new subclass of Bregman divergences and develops robust estimation and hypothesis testing procedures for both homogeneous and non-homogeneous data.

Findings

EWD estimators show competitive or superior performance to DPD estimators.

The proposed tests have well-characterized asymptotic null distributions.

The methods are applicable to both homogeneous and non-homogeneous data.

Abstract

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed. The popular density power divergence (DPD) class of estimators is a sub-class of Bregman divergences. We propose and study a new sub-class of Bregman divergences called the exponentially weighted divergence (EWD). Like the minimum DPD estimator, the minimum EWD estimator is recognised as an M-estimator. This characterisation is useful while discussing the asymptotic behaviour as well as the robustness properties of this class of estimators. Performances of the two classes are compared -- both through simulations as well as through real life examples. We develop an estimation process not only for independent and homogeneous data, but also for non-homogeneous data. General tests of parametric hypotheses based on the Bregman divergences are also considered. We establish the asymptotic null distribution of our proposed test statistic and explore its behaviour when applied to real data. The inference procedures generated by the new EWD divergence appear to be competitive or better that than the DPD based procedures.