A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that further simplify the result are considered: one in which both random vectors have the same number of components, each component taking values in an interval of unit length, and the other in which both random vectors have one component.

翻译：经典统计不等式被用于证明：两个有界随机向量的距离协方差可由其维度和界限的简单函数给出上界。本文考虑了两种能进一步简化结果的特殊情况：其一为两个随机向量分量数相同，且每个分量取值于单位长度区间内；其二为两个随机向量均仅含单一分量。