Robust error-term-scale estimate

Abstract

A scale-equivariant and regression-invariant estimator of the variance of error terms in the linear regression model is proposed and its consistency proved. The estimator is based on (down)weighting the order statistics of the squared residuals which corresponds to the consistent and scale- and regression-equivariant estimator of the regression coefficients. A small numerical study demonstrating the behaviour of the estimator under the various types of contamination is included.