Robust regression using iteratively reweighted least-squares

TLDR

Robust estimation theory has spurred demand for computational methods, and the ROSEPACK library provides weight functions that simplify implementing IRLS regression. The paper reviews computational approaches to robust linear regression, focusing on iteratively reweighted least-squares (IRLS). The authors evaluate various computational methods and emphasize IRLS as implemented in the ROSEPACK framework. The work was conducted in Cambridge, Massachusetts, with support from the National Science Foundation.

Abstract

The rapid development of the theory of robust estimation (Huber, 1973) has created a need for computational procedures to produce robust estimates. We will review a number of different computational approaches for robust linear regression but focus on one—iteratively reweighted least-squares (IRLS). The weight functions that we discuss are a part of a semi-portable subroutine library called ROSEPACK (RObust Statistical Estimation PACKage) that has been developed by the authors and Virginia Klema at the Computer Research Center of the National Bureau of Economic Research, Inc. in Cambridge, Mass. with the support of the National Science Foundation. This library (Klema, 1976) makes it relatively simple to implement an IRLS regression package.