Related papers: Distance covariance for stochastic processes
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…
Distance covariance is a widely used statistical methodology for testing the dependency between two groups of variables. Despite the appealing properties of consistency and superior testing power, the testing results of distance covariance…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
We present a test for independence of two strictly stationary time series based on a bootstrap procedure for the distance covariance. Our test detects any kind of dependence between the two time series within an arbitrary maximum lag $L$.…
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…
We introduce two new measures for the dependence of $n \ge 2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^2$-distance of quantities related to the characteristic…
The aim of this thesis is to find a solution to the non-parametric independence problem in separable metric spaces. Suppose we are given finite collection of samples from an i.i.d. sequence of paired random elements, where each marginal has…
We study an independence test based on distance correlation for random fields $(X,Y)$. We consider the situations when $(X,Y)$ is observed on a lattice with equidistant grid sizes and when $(X,Y)$ is observed at random locations. We provide…
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…
In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [Gretton et al. (2008)]) and related independence tests under the high dimensional scenario. We show that the sample…
The distance standard deviation, which arises in distance correlation analysis of multivariate data, is studied as a measure of spread. The asymptotic distribution of the empirical distance standard deviation is derived under the assumption…
This report compares two tests of second-order stationarity through simulation. It also provides several examples of localised autocovariances and their approximate confidence intervals on different real and simulated data sets. An…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
For testing two random vectors for independence, we consider testing whether the distance of one vector from a center point is independent from the distance of the other vector from a center point by a univariate test. In this paper we…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
Quantifying how distinguishable two stochastic processes are lies at the heart of many fields, such as machine learning and quantitative finance. While several measures have been proposed for this task, none have universal applicability and…
This paper proposes a new mutual independence test for a large number of high dimensional random vectors. The test statistic is based on the characteristic function of the empirical spectral distribution of the sample covariance matrix. The…