Simulation results on extensions of the Theil-Sen regression estimator

The efficiency of the the ordinary least squares (OLS) regression estimator can be very poor when the error term is normal but heteroscedastic. When the error term is nonnormal, the problem is exacerbated. Several estimators have been found to have high small-sample efficiency compared to the OLS estimator when the error term is heteroscedastic, and little efficiency is lost when in fact the error term is normal and homoscedastic. One of these is the Theil-Sen estimator with one regressor. The goal in this paper is to consider four extensions of this estimator to two regressors, one of which is found to have practical advantages over the other three. Moreover, its small-sample efficiency is found to be considerable compared to the OLS estimator, and the number of elemental subsets required to compute it is equal to the number of elemental subsets required when there is only one predictor.