Author:

Keywords:

High breakdown point, Robustness, Skewness

Abstract:

The assumption of symmetry plays a crucial role in many statistical procedures. Additionally, real world data often contain outliers. Therefore, it is important to measure the asymmetry of a sample in a way that is not a_ected by the presence of non-conforming data points. In this talk, we introduce a new robust estimator of skewness which we call the Cn. The Cn distinguishes itself among other indexes of skewness by having a much higher breakdown point. Uniquely among its competitors, the Cn quanti_es the asymmetry of a sample without reference to a particular notion of point of symmetry, yielding a more generally interpretable measure of skewness. The Cn is also supported by a fast and exact algorithm. We compare the Cn to its competitors, the quartile skewness (Hinkley, 1975) and the med-couple (Brys et al., 2004), through a simulation study and a real data example.