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Partial Distance Correlation

  • Gábor J. Székely
  • Maria L. RizzoEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 175)

Abstract

Partial distance correlation measures association between two random vectors with respect to a third random vector, analogous to, but more general than (linear) partial correlation. Distance correlation characterizes independence of random vectors in arbitrary dimension. Motivation for the definition is discussed. We introduce a Hilbert space of U-centered distance matrices in which squared distance covariance is the inner product. Simple computation of the sample partial distance correlation and definitions of the population coefficients are presented. Power of the test for zero partial distance correlation is compared with power of the partial correlation test and the partial Mantel test.

Keywords

Independence Multivariate Partial distance correlation Dissimilarity Energy statistics 

Notes

Acknowledgments

Research of the first author was supported by the National Science Foundation, while working at the Foundation.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.National Science FoundationArlingtonUSA
  2. 2.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA

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