Robustness and Distance Correlation

Oregon Convention Center 

The talk will start with a review of some earlier work on robust statistics. Attention is then focused on the distance correlation (Szekely, Rizzo, and Bakirov 2007), a popular nonparametric measure of dependence between random variables X and Y. It is related to independence of X-X' and Y-Y' where (X',Y') is an independent copy of (X,Y). The distance correlation has some robustness properties, but not all. We prove that its influence function is bounded, but that its breakdown value is zero. 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.