A Comparison of Preliminary Estimators for Robust Regression

The minimum absolute deviation (MAD) estimator may be used as an initial, or preliminary, estimator in a robust regression procedure. Alternative estimators have been developed by Hinich and Talwar (1975) and Andrews (1974). All three estimators are related to the median, and so their respective asymptotic properties can be compared relatively easily, at least in simple models. The conclusion which emerges from such comparisons is that the asymptotic properties of the MAD estimator are, in general, superior to those of the other two estimators. However, certain small-sample properties are also important in assessing the relative merits of the different estimators.