Density Power Downweighting and Robust Inference: Some New Strategies

TL;DR

This paper introduces a new family of Bregman divergences that generalizes density power divergence, aiming to improve the robustness-efficiency trade-off in statistical inference procedures.

Contribution

It proposes a superfamily of divergences that enhances robustness and efficiency in statistical inference, extending the existing density power divergence framework.

Findings

New divergence family encompasses density power divergence

Inference procedures based on this family improve robustness

The approach offers a better robustness-efficiency balance

Abstract

Preserving the robustness of the procedure has, at the present time, become almost a default requirement for statistical data analysis. Since efficiency at the model and robustness under misspecification of the model are often in conflict, it is important to choose such inference procedures which provide the best compromise between these two concepts. Some minimum Bregman divergence estimators and related tests of hypothesis seem to be able to do well in this respect, with the procedures based on the density power divergence providing the existing standard. In this paper we propose a new family of Bregman divergences which is a superfamily encompassing the density power divergence. This paper describes the inference procedures resulting from this new family of divergences, and makes a strong case for the utility of this divergence family in statistical inference.