Robust Regression Computation Using Iteratively Reweighted Least Squares

Abstract

Several variants of Newton’s method are used to obtain estimates of solution vectors and residual vectors for the linear model $Ax = b + e = b_{true} $ using an iteratively reweighted least squares criterion, which tends to diminish the influence of outliers compared with the standard least squares criterion. Algorithms appropriate for dense and sparse matrices are presented. Solving Newton’s linear system using updated matrix factorizations or the (unpreconditioned) conjugate gradient iteration gives the most effective algorithms. Four weighting functions are compared, and results are given for sparse well-conditioned and ill-conditioned problems.