Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11005594 | Journal of Multivariate Analysis | 2018 | 21 Pages |
Abstract
We propose three new measures of mutual dependence between multiple random vectors. Each measure is zero if and only if the random vectors are mutually independent. The first generalizes distance covariance from pairwise dependence to mutual dependence, while the other two measures are sums of squared distance covariances. The proposed measures share similar properties and asymptotic distributions with distance covariance, and capture non-linear and non-monotone mutual dependence between the random vectors. Inspired by complete and incomplete V-statistics, we define empirical and simplified empirical measures as a trade-off between the complexity and statistical power when testing mutual independence. The implementation of corresponding tests is demonstrated by both simulation results and real data examples.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
Ze Jin, David S. Matteson,