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.

摘要

当不满足误差项的一些分布假设时，可以使用经验似然（EL）估计方法来估计线性回归模型的参数。在EL过程中，使用正态假设下的最大似然（ML）估计方法的似然分数来形成约束。但是，由于正态性假设下的ML估计量由于得分函数的无穷大而受到异常值的极大影响，因此，从ML得分函数借来的具有时间限制的EL估计值也将被异常值所破坏。本文针对线性回归模型的参数，提出了鲁棒的经验似然估计器。将使用从MM估计方程式借来的鲁棒性约束来完成这种鲁棒性。