A Robust Adaptive Modified Maximum Likelihood Estimator for the Linear Regression Model

TL;DR

This paper introduces RAMML, a new robust estimator for linear regression that effectively handles both y and x outliers, outperforming existing methods in simulations and real data applications.

Contribution

The paper proposes a novel RAMML estimator that enhances robustness of adaptive modified maximum likelihood estimation against leverage points in linear regression.

Findings

RAMML outperforms existing estimators in mean squared error.

Simulation results favor RAMML in various settings.

Real data analysis demonstrates practical applicability.

Abstract

In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with this situation and thus they are widely used in practice. One example of robust estimators for regression are adaptive modified maximum likelihood (AMML) estimators (Donmez, 2010). However, they are not robust to $x$ outliers, so-called leverage points. In this study, we propose a new regression estimator by employing an appropriate weighting scheme in the AMML estimation method. The resulting estimator is called robust AMML (RAMML) since it is not only robust to y outliers but also to x outliers. A simulation study is carried out to compare the performance of the RAMML estimator with some existing robust estimators such as MM, least trimmed squares (LTS) and S. The results show that the RAMML estimator is preferable in most settings according to the mean squared error (MSE) criterion. Two data sets taken from the literature are also analyzed to show the implementation of the RAMML estimation methodology.