A Parametric Framework for the Comparison of Methods of Very Robust Regression

TL;DR

This paper introduces a parametric framework using a parameter λ to systematically compare the behavior of various very robust regression estimators, analyzing their variance, bias, and outlier detection power.

Contribution

It presents a novel parametric approach to study and compare robust regression methods by examining their properties along a defined model path.

Findings

Analyzed variance and bias of five estimators as a function of λ.

Evaluated the outlier detection power of the estimators.

Provided insights into the estimators' behavior as data groups move closer or farther apart.

Abstract

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression data and the outliers. We introduce a parameter $\lambda$ that defines a parametric path in the space of models and enables us to study, in a systematic way, the properties of estimators as the groups of data move from being far apart to close together. We examine, as a function of $\lambda$, the variance and squared bias of five estimators and we also consider their power when used in the detection of outliers. This systematic approach provides tools for gaining knowledge and better understanding of the properties of robust estimators.