Related papers: Distance multivariance: New dependence measures fo…
In this paper we study bounds for the total variation distance between two second degree polynomials in normal random variables provided that they essentially depend on at least three variables.
Labelled Markov chains (LMCs) are widely used in probabilistic verification, speech recognition, computational biology, and many other fields. Checking two LMCs for equivalence is a classical problem subject to extensive studies, while the…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
The multivariate Hilbert-Schmidt-Independence-Criterion (dHSIC) and distance multivariance allow to measure and test independence of an arbitrary number of random vectors with arbitrary dimensions. Here we define versions which only depend…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample…
Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous…
Distance covariance and distance correlation have been widely adopted in measuring dependence of a pair of random variables or random vectors. If the computation of distance covariance and distance correlation is implemented directly…
Regular variation is often used as the starting point for modeling multivariate heavy-tailed data. A random vector is regularly varying if and only if its radial part $R$ is regularly varying and is asymptotically independent of the angular…
We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
Given an iid sequence of pairs of stochastic processes on the unit interval we construct a measure of independence for the components of the pairs. We define distance covariance and distance correlation based on approximations of the…
Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…
Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the…
We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…
A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…
In recent years, a variety of novel measures of dependence have been introduced being capable of characterizing diverse types of directed dependence, hence diverse types of how a number of predictor variables $\mathbf{X} = (X_1, \dots,…
We propose a new multivariate dependency measure. It is obtained by considering a Gaussian kernel based distance between the copula transform of the given d-dimensional distribution and the uniform copula and then appropriately normalizing…
Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring…