A New Measure of Dependence Between Continuous and Multinomial Random Variables
arXiv:2607.27381
The paper proposes a new dependence measure for a continuous variable and a multinomial variable based on the Hellinger distance between conditional distributions, and provides an estimator with a √n convergence rate for inference and independence testing.
Abstract
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.