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Activity Number: 313 - Recent Developments in Statistical Inference Using Distance Correlation and Related Dependence Metrics
Type: Invited
Date/Time: Tuesday, July 30, 2019 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #300001
Title: Distance-Based and RKHS-Based Dependence Metrics in High Dimension
Author(s): Xiaofeng Shao*
Companies: University of Illinois At Urbana-Champaign
Keywords: Independence testing; U-statistic; High dimension; Distance Covariance

Distance covariance and distance correlation are well known to completely characterize the independence between two random vectors of fixed dimensions. In this talk, we show that the sample distance covariance between two random vectors can be approximated by the sum of squared componentwise sample cross-covariances up to an asymptotically constant factor, which indicates that the distance covariance based test can only capture linear dependence in high dimension. As a consequence, the distance correlation based t test developed by Szekely and Rizzo (2013) for independence is shown to have trivial limiting power when the two random vectors are nonlinearly dependent but component-wisely uncorrelated. This new and surprising phenomenon, which seems to be discovered for the first time, is further confirmed in our simulation studies. The same phenomenon also holds for the Hilbert-Schmidt independence criterion in the high dimension low sample size setting. A remedy based on aggregation of marginal sample distance covariances is proposed and compared in the simulation studies.

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

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