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Activity Number: 634 - Recent Advancements in Distance and Kernel-Based Metrics and Related Learning Methods
Type: Invited
Date/Time: Thursday, August 1, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #300150
Title: Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence via Complete and Incomplete V-Statistics
Author(s): David Matteson* and Ze Jin
Companies: Cornell University and Facebook
Keywords: Characteristic functions; Distance covariance; Multivariate analysis; Mutual independence; V-statistics

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.

Authors who are presenting talks have a * after their name.

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