Robust L estimation of scale with an application in astronomy

Abstract

In this article, we investigate the robustness properties of a class of L estimators of scale and then develop robust procedures for making inferences about scale. We pay particular attention to trimmed estimators that should perform well when the underlying model is Gaussian. We find that trimmed versions of the efficient linear L estimator for the Gaussian distribution perform better than trimmed standard deviation estimators. We then apply a trimmed version of the efficient linear L estimator for the Gaussian distribution to astronomical data.