### 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 language | English (US) |
---|---|

Pages (from-to) | 829-843 |

Number of pages | 15 |

Journal | Biometrika |

Volume | 104 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2017 |

### Fingerprint

### 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

*Biometrika*,

*104*(4), 829-843. https://doi.org/10.1093/biomet/asx043

}

*Biometrika*, vol. 104, no. 4, pp. 829-843. https://doi.org/10.1093/biomet/asx043

**Projection correlation between two random vectors.** / Zhu, Liping; Xu, Kai; Li, Runze; Zhong, Wei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Projection correlation between two random vectors

AU - Zhu, Liping

AU - Xu, Kai

AU - Li, Runze

AU - Zhong, Wei

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85039170100&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85039170100&partnerID=8YFLogxK

U2 - 10.1093/biomet/asx043

DO - 10.1093/biomet/asx043

M3 - Article

C2 - 29430040

AN - SCOPUS:85039170100

VL - 104

SP - 829

EP - 843

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 4

ER -