We propose a nonparametric two-sample test procedure based on Maximum Mean
Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same …

Energy distance is a statistical distance between the distributions of random vectors, which
characterizes equality of distributions. The name energy derives from Newton's gravitational …

Testing independence between high-dimensional random vectors is fundamentally different
from testing independence between univariate random variables. Taking the projection …

The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii)
the independence between two high-dimensional random vectors. We show that the energy …

In nonparametric independence testing, we observe iid data {(Xi, Yi)} ni= 1, where X∈ Χ,
Y∈ Y lie in any general spaces, and we wish to test the null that X is independent of Y …

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-
scale data, we study the asymptotic behaviour of kernel two-sample tests when the …

Distance correlation has become an increasingly popular tool for detecting the nonlinear
dependence between a pair of potentially high-dimensional random vectors. Most existing …

Rank-based indices for testing independence between two high-dimensional vectors Page 1
The Annals of Statistics 2024, Vol. 52, No. 1, 184–206 https://doi.org/10.1214/23-AOS2339 © …

Testing for independence plays a fundamental role in many statistical techniques. Among
the nonparametric approaches, the distance-based methods (such as the distance …

Since the pioneering work of sliced inverse regression, sufficient dimension reduction has
been growing into a mature field in statistics and it has broad applications to regression …