AI 中文总结
本文提出一种基于Hellinger距离的连续与多项随机变量依赖度量，开发了结合数据拆分与核密度估计的估计量，其收敛速率为√n，可便捷构造置信区间与独立性检验。
AI 中文摘要
本文提出了一种新的连续随机变量与多项随机变量之间的依赖关系度量方法，该方法基于条件分布之间的Hellinger距离，满足依赖度量的理想特性，无需对连续随机变量做特定分布假设，也不假设离散随机变量源于潜在连续随机变量。本文开发了一种基于数据拆分和核密度估计的依赖度量估计量，该估计量的渐近分布形式简单，收敛速率为√n，使得依赖度量的置信区间和独立性检验易于实现且计算便捷。
英文摘要
A novel measure of dependence between a continuous random variable and a multinomial random variable is introduced. The proposed measure is based on the Hellinger distance between conditional distributions. It satisfies the desiderata for a dependence measure without making specific distributional assumptions about the continuous random variable or assuming that the discrete random variable arises from a latent continuous random variable. An estimator of the dependence measure based on data splitting and kernel density estimation is developed. The asymptotic distribution of the estimator has a simple form with a convergence rate of \sqrt{n}, making confidence intervals for the dependence measure and a test for independence straightforward and computationally convenient.
