Bias robustness of three median-based regression estimates

The need for regression estimates with small biases has been highlighted in view of the renewed interest in robust inference beyond point estimation. Estimates with small biases are essential for stable and informative robust inference. In this paper we study the bias performance of three median-based estimates: Brown and Mood (1951) estimate, Theil (1950) and Sen (1968) estimate and Siegel's repeated median (1982), which exhibits an outstanding bias performance. We also consider a one-step version of the Brown and Mood estimate. We pay special attention to the maximum asymptotic bias of the intercept parameter which has been mostly ignored in the robustness literature (with exceptions pointed out in the introduction). (C) 2003 Elsevier B.V. All rights reserved.