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Activity Number: 201
Type: Contributed
Date/Time: Monday, August 1, 2016 : 10:30 AM to 11:15 AM
Sponsor: Section on Nonparametric Statistics
Abstract #321800
Title: Measuring and Testing Mutual Multivariate Independence Based on Distance Covariance
Author(s): Ze Jin* and David Matteson
Companies: Cornell University and Cornell University
Keywords: characteristic functions ; distance covariance ; mutual independence ; U-statistics

We propose two measures of mutual multivariate independence for random vectors based on distance covariance. Both measures are zero if and only if the random vectors are mutually independent, capturing nonlinear dependence structure among the random vectors. The first measure is a sum of pairwise distance covariance measure. While the second measure is a natural generalization of distance covariance from pairwise independence to mutual independence, and inherits many nice properties of distance covariance. Empirical measures are defined as U-statistics using certain Euclidean distances between sample elements. Their asymptotic properties and applications in testing mutual independence are discussed. Implementation of the tests is demonstrated by real data examples and simulation results are presented.

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

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