A Variant of Huber Robust Regression

In this paper, we develop a variant of Huber robust regression. Our approach is inspired by Huber's $M$ estimates; however, we deal with the scale estimate differently. The class of estimators we develop includes least squares and least absolute residuals as limiting cases and can be considered as a generalization of the trimmed mean to regression. We exhibit an algorithm to compute these estimates and prove its correctness. Also, we show how to extend our estimators to include weighting, equality and inequality constraints, and the addition or deletion of data points.