Combining empirical likelihood and robust estimation methods for linear regression models

Abstract

Ordinary least square (OLS) and robust methods are used for estimating the parameters of a linear regression model. These methods perform well under some distributional assumptions which may not be appropriate for some data sets. Therefore, nonparametric methods like Empirical likelihood (EL) may be considered. The EL method maximizes an EL function under some constraints. We consider the EL method with robustified constraints using M estimation method. We provide a small simulation study and a real data example to demonstrate the capability of robust EL method and results reveal that robust constraints are needed when outliers are resent in data.