Efficient Bounded-Influence Regression Estimation

Abstract The least squares estimator for β in the classical linear regression model is strongly efficient under certain conditions. However, in the presence of heavy-tailed errors and/or anomalous data, the least squares efficiency can be markedly reduced. In this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first-order condition for strong efficiency subject to the constraint. We then show that the estimator is asymptotically normal. The article concludes with an outline of an algorithm for computing a bounded-influence regression estimator and with an example comparing least squares, robust regression as developed by Huber, and the estimator proposed in this article.