The Performance of Robust Regression Estimators in Presence of Outliers

Amer, Amer Ibrahim; Abd Albary, Rowaida Ali; Salem, Salem Adel; Abd-Elftah, Ahmed Ibrahim

doi:10.21608/erurj.2024.279277.1137

The Performance of Robust Regression Estimators in Presence of Outliers

Document Type : Review article

Authors

¹ Department of Business Technology, Faculty of Management, Economics, and Business Technology, Egyptian Russian University, Badr City, Cairo, Egypt

² Department of Business Technology, Faculty of Management, Economics, and Business Technology, Egyptian Russian University, Badr City, Cairo, Egypt.

10.21608/erurj.2024.279277.1137

Abstract

Linear regression models are common, powerful statistical methods used to build a model between a dependent variable and one or more independent variables to explain and validate the relationship between the dependent variable and the independent variables the parameters of the linear regression model are unknown. Estimators are derived to estimate those parameters. Ordinary Least Square (OLS) is one of the most common estimates for the linear regression parameters since it is the best linear unbiased estimator (BLUE) under certain assumptions. The occurrence of outliers in the data leads OLS to have a poor fit and misleading results. Robust estimates are designed to handle the presence of outliers by different methods, among many robust estimates developed over the years, the most common and efficient estimates are discussed. The results indicate that among the different estimates MM estimate had superiority over OLS and other robust estimates, leading to the conclusion that the presence of outliers could lead to many consequences, checking for their presence and handling them appropriately is the most efficient fitting.

Keywords