Robust Inference Using the Exponential-Polynomial Divergence

TL;DR

This paper introduces a generalized divergence method for robust statistical inference that extends the density power divergence, offering improved robustness and efficiency trade-offs without needing kernel smoothing.

Contribution

It proposes a new divergence framework that generalizes the density power divergence, enhancing robustness and efficiency in parametric inference.

Findings

The generalized divergence includes DPD as a special case.

New divergence options improve robustness-efficiency balance.

Method avoids non-parametric smoothing techniques.

Abstract

Density-based minimum divergence procedures represent popular techniques in parametric statistical inference. They combine strong robustness properties with high (sometimes full) asymptotic efficiency. Among density-based minimum distance procedures, the methods based on the Bregman-divergence have the attractive property that the empirical formulation of the divergence does not require the use of any non-parametric smoothing technique such as kernel density estimation. The methods based on the density power divergence (DPD) represent the current standard in this area of research. In this paper, we will present a more generalized divergence that subsumes the DPD as a special case and produces several new options providing better compromises between robustness and efficiency.