Median-Product Regression Estimators: New Robust Estimators for Bivariate Data

Abstract

In this article we consider the problem of calculating the linear regression estimates from bivariate data containing a fraction of outliers.
Classical estimates of slope and intercept are affected by outliers, while robust estimates are computationally inefficient. In order to achieve
robustness and computational efficiency at the same time, we propose new robust estimators of regression parameters. We call our estimators
Median-Product (MP) regression estimators. To construct the proposed MP estimators, we replaced the non-robust building blocks of
classical OLS estimators by their robust counterparts. Thus, we developed robust regression estimators that do not use iterative algorithm.
Our simulation studies and real data application show that the proposed MP estimators give better results in the contaminated data compared
to the classical estimators. The performance of our estimators is similar to that of the existing robust estimators. The advantage of our
estimators is that they require less computing time than the existing robust estimators.