# Robustness analysis of a Maximum Correntropy framework for linear regression

## TL;DR

This paper presents a unified framework for robust linear regression using correntropy maximization, analyzing its robustness properties and providing bounds on estimation errors, with numerical illustrations of special cases.

## Contribution

It introduces a general correntropy-based regression framework that encompasses Gaussian and Laplacian kernels, and analyzes its robustness and stability properties.

## Key findings

- Bounded estimation error under certain conditions
- Explicit error bounds derived and discussed
- Numerical studies of special cases included

## Abstract

In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based correntropy estimators as special cases. An analysis of the robustness properties is then provided. The analysis includes a quantitative characterization of the informativity degree of the regression which is appropriate for studying the stability of the estimator. Using this tool, a sufficient condition is expressed under which the parametric estimation error is shown to be bounded. Explicit expression of the bound is given and discussion on its numerical computation is supplied. For illustration purpose, two special cases are numerically studied.