Least absolute deviations regression resists outliers in the response variable but is relatively sensitive to outlying observations in the explanatory variables. In this paper a simple solution is proposed to overcome this problem. This is achieved by minimizing the absolute values of vertical...

We propose partially adaptive estimators of the trimming proportion [alpha] for the trimmed mean in the location modeling and for the trimmed least-squares estimator of Koenker and Bassett (1978) in the linear regression model. The adaptive estimators are based on Hájek's (1970) rank-based...