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