Efficient Robust Estimation of Regression Models (Replaced by DP 2007-87)

This paper introduces a new class of regression estimators robust to outliers, measurement errors, and other data irregularities.The estimators are based on the twostep least weighted squares method, where weights are adaptively computed using the empirical distribution function of regression residuals obtained from an initial robust fit.The asymptotic distribution of the proposed estimators is derived under general conditions, allowing for time-series applications.Further, it is shown that the breakdown point of the proposed estimators equals that of the initial robust estimate.The main contribution of the work is that the proposed two-step procedures combine several desirable properties, which different existing estimators posses separately, but not jointly.These properties are asymptotic efficiency if the errors are normally distributed, high breakdown point achieved without rejecting (trimming) of observations, and independence of auxiliary tuning parameters.A Monte Carlo study shows that the two-step least weighted squares outperform in most situations both least squares and existing robust estimators in finite samples.