The concept of distance covariance/correlation was introduced recently to characterise
dependence among vectors of random variables. We review some statistical aspects of …

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 …

In this paper, we study distance covariance, Hilbert–Schmidt covariance (aka Hilbert–
Schmidt independence criterion [In Advances in Neural Information Processing Systems …

This paper is concerned with test of the conditional independence. We first establish an
equivalence between the conditional independence and the mutual independence. Based …

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 …

We introduce an independence criterion based on entropy regularized optimal transport.
Our criterion can be used to test for independence between two samples. We establish non …

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

Kernel techniques are among the most popular and powerful approaches of data science.
Among the key features that make kernels ubiquitous are (i) the number of domains they …

Carbon pricing is one of the key policy tools in the green recovery of the post-COVID-19 era.
As linkages among ETSs worldwide are future trend, the carbon price spillover effects …

Identifying interactions and understanding the underlying generating mechanism is
essential for interpreting the response of black‐box models. We offer a systematic analysis …