Trimmed least squares estimator as best trimmed linear conditional estimator for linear regression model

Abstract

A class of trimmed linear conditional estimators based on regression quantiles for the linear regression model is introduced. This class serves as a robust analogue of non-robust linear unbiased estimators. Asymptotic analysis then shows that the trimmed least squares estimator based on regression quantiles (Koenker and Bassett (1978)) is the best in this estimator class in terms of asymptotic covariance matrices. The class of trimmed linear conditional estimators contains the Mallows-type bounded influence trimmed means (see De Jongh et al (1988)) and trimmed instrumental variables estimators. A large sample methodology based on trimmed instrumental variables estimator for confidence ellipsoids and hypothesis testing is also provided.