A0324
Title: Is distance correlation robust?
Authors: Jakob Raymaekers - University of Antwerp (Belgium)
Sarah Leyder - University of Antwerp (Belgium) [presenting]
Peter Rousseeuw - KU Leuven (Belgium)
Abstract: Distance correlation is a popular measure of dependence between random variables. It has some robustness properties, but not all of them. We prove that the influence function of the usual distance correlation is bounded but that its breakdown value is zero. Moreover, it has an unbounded sensitivity function, converging to the bounded influence function for increasing sample size. To address this sensitivity to outliers, we construct a more robust version of distance correlation, which is based on a new data transformation. Simulations indicate that the resulting method is quite robust and has good power in the presence of outliers. We illustrate the method on genetic data. Comparing the classical distance correlation with its more robust version provides additional insight.
