  Ordinary least square (OLS), maximum likelihood (ML) and robust methods are
the widely used methods to estimate the parameters of a linear regression
model. It is well known that these methods perform well under some
distributional assumptions on error terms. However, these distributional
assumptions on the errors may not be appropriate for some data sets. In these
case, nonparametric methods may be considered to carry on the regression
analysis. Empirical likelihood (EL) method is one of these nonparametric
methods. The EL method maximizes a function, which is multiplication of the
unknown probabilities corresponding to each observation, under some constraints
inherited from the normal equations in OLS estimation method. However, it is
well known that the OLS method has poor performance when there are some
outliers in the data. In this paper, we consider the EL method with robustifyed
constraints. The robustification of the constraints is done by using the robust
M estimation methods for regression. We provide a small simulation study and a
real data example to demonstrate the capability of the robust EL method to
handle unusual observations in the data. The simulation and real data results
reveal that robust constraints are needed when heavy tailedness and/or outliers
are possible in the data.
