Numerical Methods for Robust Regression: Linear Models

This paper considers the robust regression problem, in which observations with large residuals are given less weight in the analysis. An auxiliary scale estimate is needed in this problem to define which residuals are large. We develop variants of Newton’s method which allow for simultaneous adjustment of the scale factor and regression coefficients, and which converge superlinearily to both estimates for different loss functions. Computational results are given for both the Huber and biweight loss functions with scales obtained from the median absolute residual and the Winsorized residual variance.