A New Family of Divergences Originating from Model Adequacy Tests and Application to Robust Statistical Inference

TL;DR

This paper introduces a new family of divergences derived from tubular model adequacy tests, enhancing robust statistical inference, and explores their properties and applications, while highlighting limitations of traditional influence function analysis.

Contribution

It develops a larger superfamily of divergences from model adequacy tests, expanding tools for robust inference and analyzing their properties.

Findings

The new divergences improve robustness in statistical inference.

The superfamily of divergences extends existing $S$-divergences.

First order influence function analysis fails to capture robustness of these methods.

Abstract

Minimum divergence methods are popular tools in a variety of statistical applications. We consider tubular model adequacy tests, and demonstrate that the new divergences that are generated in the process are very useful in robust statistical inference. In particular we show that the family of $S$-divergences can be alternatively developed using the tubular model adequacy tests; a further application of the paradigm generates a larger superfamily of divergences. We describe the properties of this larger class and its potential applications in robust inference. Along the way, the failure of the first order influence function analysis in capturing the robustness of these procedures is also established.