Robust Distance Covariance 1
研究了距离协方差的稳健性，发现其影响函数有界但崩溃值为零，并基于新数据变换构造了更稳健的距离协方差和距离相关方法，模拟和遗传数据表明该方法在存在异常值时效果良好。
Summary Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance 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 covariance and distance correlation, 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.