Theory and methods: Small sample performance of extreme regression quantiles
In this paper we studied the finite sample behaviour of a range of estimators for extreme regression quantiles. We studied the behaviour of the estimators over a wide range of heavy tailed error distributions and design matrices containing influential design points. Our main conclusion is that restricted bounded influence estimators should be the estimators of choice. In particular the preferred estimator is a restricted bounded influence Koenker-Bassett based on a common slope estimator of a 20% trimmed mean. This estimator has good performance in well-behaved cases and protects one against the adverse effects of heavy tails and high leverage design points.