# Measuring and testing dependence by correlation of distances

@article{Szekely2007MeasuringAT, title={Measuring and testing dependence by correlation of distances}, author={G'abor J. Sz'ekely and Maria L. Rizzo and Nail K. Bakirov}, journal={Annals of Statistics}, year={2007}, volume={35}, pages={2769-2794} }

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the…

## 1,882 Citations

### Partial Distance Correlation

- Mathematics
- 2016

Partial distance correlation measures association between two random vectors with respect to a third random vector, analogous to, but more general than (linear) partial correlation. Distance…

### Conditional Distance Variance and Correlation

- Mathematics, Economics
- 2012

Recently a new dependence measure, the distance correlation, has been proposed to measure the dependence between continuous random variables. A nice property of this measure is that it can be…

### Partial Distance Correlation with Methods for Dissimilarities

- Computer Science
- 2013

This work defines the partial distance correlation statistics with the help of a new Hilbert space where the squared distance covariance is the inner product, and develops and implements a test for zero partialdistance correlation.

### Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics

- Computer Science, MathematicsJ. Multivar. Anal.
- 2018

### The distance correlation t-test of independence in high dimension

- Mathematics, Computer ScienceJ. Multivar. Anal.
- 2013

### Brownian distance covariance

- Mathematics
- 2009

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation…

### On Possibilistic Version of Distance Covariance and Correlation

- Computer ScienceTrends in Mathematics and Computational Intelligence
- 2018

The possibilistic distance correlation is defined, each \(\gamma \)-level set of the joint possibility distribution is equipped with a uniform probability distribution, and the probabilistic distance covariance and correlation between the marginal distributions are determined.

### Distance covariance for stochastic processes

- Computer Science, Mathematics
- 2017

An analogs of the distance covariance for two stochastic processes defined on some interval is proposed, which can be used to test the independence of two processes.

### Distance Metrics for Measuring Joint Dependence with Application to Causal Inference

- Computer Science, MathematicsJournal of the American Statistical Association
- 2019

The high-order distance covariance is introduced to measure the so-called Lancaster interaction dependence and is defined as a linear combination of pairwise distance covariances and their higher-order counterparts which together completely characterize mutual independence.

### Measuring Linear Correlation Between Random Vectors

- MathematicsInformation Sciences
- 2022

We introduce a new scalar coefficient to measure linear correlation between random vectors which preserves all the relevant properties of Pearson’s correlation in arbitrary dimensions. The new…

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