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Activity Number: 631 - Recent Developments in Statistical Inference Using Distance Correlation and Related Dependence Metrics
Type: Invited
Date/Time: Thursday, August 3, 2017 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #321917
Title: Why Classical Measures of Dependence Do Not Satisfy Their Natural Axioms?
Author(s): Gabor J Szekely*
Companies: National Science Foundation
Keywords: dependence measures ; correlation ; maximal correlation ; maximal information coefficient ; axioms ; distance correlation

In this talk four natural axioms of dependent measures D(X,Y)for Hilbert space valued random variables X and Y will be stated: (i) D(X,Y) = 0 iff X and Y are independent, (ii) D(X,X) = 1, (iii) D is invariant with respect to similarity transformations of the Hilbert space, (iv)D is continuous with respect to weak convergence of bounded sequences of random variables. --- We will see that classical measures of dependence, like correlation, maximal correlation, etc. do not satisfy some of these axioms. The same holds for the newly introduced maximal information coefficient. Distance correlation introduced by the speaker twelve years ago does satisfy all axioms above.

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

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