On the maxbias curve of residual admissible robust regression estimates

Abstract

The robustness properties of a regression estimate are throughly described by its maxbias curve. However, this function is difficult to compute, especially when the regressors are not elliptically distributed. In this paper, we propose a general method for computing maxbias curves, valid for a large number of robust regression estimates, namely, those estimates defined by residual admissible functionals. Our results are also useful to compute maxbias curves when the regressors are not elliptically distributed. \Ve provide several examples of application of the method which include S-, T-, and signed R-estimates. MM-estimates are also studied under a related, although slightly different, approach.