Significance Regression: Robust Regression for Collinear Data

Abstract

This paper examines robust linear multivariable regression from collinear data. A brief review of M-estimators discusses the strengths of this approach for tolerating outliers and/or perturbations in the error distributions. The review reveals that M-estimation may be unreliable if the data exhibit collinearity. Next, significance regression (SR) is discussed. SR is a successful method for treating collinearity but is not robust. A new significance regression algorithm for the weighted-least-squares error criterion (SR-WLS) is developed. Using the weights computed via M-estimation with the SR-WLS algorithm yields an effective method that robustly mollifies collinearity problems. Numerical examples illustrate the main points.