Projection correlation between two random vectors

Liping Zhu, Kai Xu, Runze Li, Wei Zhong

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We propose the use of projection correlation to characterize dependence between two random vectors. Projection correlation has several appealing properties. It equals zero if and only if the two random vectors are independent, it is not sensitive to the dimensions of the two random vectors, it is invariant with respect to the group of orthogonal transformations, and its estimation is free of tuning parameters and does not require moment conditions on the random vectors. We show that the sample estimate of the projection correction is n-consistent if the two random vectors are independent and root-n-consistent otherwise. Monte Carlo simulation studies indicate that the projection correlation has higher power than the distance correlation and the ranks of distances in tests of independence, especially when the dimensions are relatively large or the moment conditions required by the distance correlation are violated.

Original languageEnglish (US)
Pages (from-to)829-843
Number of pages15
JournalBiometrika
Volume104
Issue number4
DOIs
StatePublished - Dec 1 2017

Fingerprint

Random Vector
Projection
Moment Conditions
Test of Independence
Orthogonal Transformation
Parameter Tuning
High Power
Monte Carlo Simulation
Tuning
Roots
Simulation Study
If and only if
Invariant
Zero
Estimate
testing
sampling
Moment conditions

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Zhu, Liping ; Xu, Kai ; Li, Runze ; Zhong, Wei. / Projection correlation between two random vectors. In: Biometrika. 2017 ; Vol. 104, No. 4. pp. 829-843.
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Projection correlation between two random vectors. / Zhu, Liping; Xu, Kai; Li, Runze; Zhong, Wei.

In: Biometrika, Vol. 104, No. 4, 01.12.2017, p. 829-843.

Research output: Contribution to journalArticle

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