Statistics

Computer science

Least-squares function approximation

Least trimmed squares

Regression

Pattern recognition (psychology)

Mathematics

Estimator

Generalized least squares

Partial least squares regression

Robust regression

Artificial intelligence

Iteratively reweighted least squares

Total least squares

Communication in Statistics- Theory and Methods

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.

Robust regression using iteratively reweighted least-squares