标题： 微分距离相关性及其应用 显示英文标题

标题： Differential Distance Correlation and Its Applications

摘要： 在本文中，我们提出了一种新的系数，称为差分距离相关性，用于衡量随机变量$ Y \in \mathbb {R} $与随机向量$ X \in \mathbb {R}^{p} $之间依赖性的强度。 该系数具有简洁的表达式，并且对随机向量的任意正交变换不变。 此外，该系数是简单且可解释的依赖度量的强一致估计量，当且仅当$ X $与$ Y $独立时为 0，并且当且仅当$ Y $几乎必然确定$ X $时为 1。 此外，在独立假设下，该系数在简单的方差下表现出渐近正态性，便于快速准确地计算检验独立性的 p 值。 两个模拟实验表明，我们提出的系数在识别具有更高振荡行为的关系方面优于一些依赖度量。 我们还将我们的方法应用于分析一个实际数据示例。 显示英文摘要

摘要： In this paper, we propose a novel coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb {R} $ and a random vector $ X \in \mathbb {R}^{p} $. The coefficient has a concise expression and is invariant to arbitrary orthogonal transformations of the random vector. Moreover, the coefficient is a strongly consistent estimator of a simple and interpretable dependent measure, which is 0 if and only if $ X $ and $ Y $ are independent and equal to 1 if and only if $ Y $ determines $ X $ almost surely. Furthermore, the coefficient exhibits asymptotic normality with a simple variance under the independent hypothesis, facilitating fast and accurate estimation of p-value for testing independence. Two simulated experiments demonstrate that our proposed coefficient outperforms some dependence measures in identifying relationships with higher oscillatory behavior. We also apply our method to analyze a real data example.