Empirical likelihood-MM (EL-MM) estimation for the parameters of a linear regression model

Abstract

ABSTRACT Parameters of a linear regression model can be estimated using empirical likelihood (EL) estimation method when some distributional assumptions on error term are not satisfied. In the EL procedure constrains are formed using the likelihood scores of maximum likelihood (ML) estimation method under normality assumption. However, since the ML estimators under normality assumption are dramatically affected from outliers due to unboundedness of the score function the resulting EL estimators with the moment restrictions borrowed from the ML score functions will also be ruined by outliers. In this paper, robust empirical likelihood estimators for the parameters of a linear regression model are proposed. This robustification will be done using robust constraints borrowed from the MM estimating equation. Simulation results and real data examples show that the performance of the proposed EL-MM estimator is remarkably superior to the performance of classical EL estimator when there are outliers in response and/or explanatory variables.