Abstract

One of the most basic needs of an applied scientist in any analysis involving real data is a robust estimator of location. The sample mean, the most common estimator of location, is notoriously non-robust under the presence of outliers, which hinders its applicability in spite of its simplicity and all its efficiency properties. More sophisticated robust estimators often achieve their robustness at the cost of the simplicity and appeal of the sample mean. In this paper, we study the robustness properties of the generalized mean, a simple variant of the usual arithmetic mean and show that, together with a suitable tuning parameter selection strategy, the generalized mean can function as a simple, intuitive and robust estimator of the population location.