Robust Weighted Lad Regression

The least squares linear regression estimator is well-known to be highly sensitive tounusual observations in the data, and as a result many more robust estimators havebeen proposed as alternatives. One of the earliest proposals was least-sum of absolutedeviations (LAD) regression, where the regression coefficients are estimated throughminimization of the sum of the absolute values of the residuals. LAD regression hasbeen largely ignored as a robust alternative to least squares, since it can be stronglyaffected by a single observation (that is, it has a breakdown point of 1/n, where n isthe sample size). In this paper we show that judicious choice of weights can resultin a weighted LAD estimator with much higher breakdown point. We discuss the properties of the weighted LAD estimator, and show via simulation that its performance is competitive with that of high breakdown regression estimators, particularly in thepresence of outliers located at leverage points. We also apply the estimator to several real data sets