IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v104y2017i4p829-843..html
   My bibliography  Save this article

Projection correlation between two random vectors

Author

Listed:
  • Liping Zhu
  • Kai Xu
  • Runze Li
  • Wei Zhong

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.

Suggested Citation

  • Liping Zhu & Kai Xu & Runze Li & Wei Zhong, 2017. "Projection correlation between two random vectors," Biometrika, Biometrika Trust, vol. 104(4), pages 829-843.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:4:p:829-843.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/asx043
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mirosław Krzyśko & Łukasz Smaga, 2024. "Application of distance standard deviation in functional data analysis," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 18(2), pages 431-454, June.
    2. Tan, Weng Cheong & Saw, Lip Huat & Thiam, Hui San & Xuan, Jin & Cai, Zuansi & Yew, Ming Chian, 2018. "Overview of porous media/metal foam application in fuel cells and solar power systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 96(C), pages 181-197.
    3. L Weihs & M Drton & N Meinshausen, 2018. "Symmetric rank covariances: a generalized framework for nonparametric measures of dependence," Biometrika, Biometrika Trust, vol. 105(3), pages 547-562.
    4. Xu, Kai & Zhou, Yeqing, 2021. "Projection-averaging-based cumulative covariance and its use in goodness-of-fit testing for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    5. Pedro H. C. Sant'Anna & Xiaojun Song, 2020. "Specification tests for generalized propensity scores using double projections," Papers 2003.13803, arXiv.org, revised Apr 2023.
    6. Fan, Jinlin & Zhang, Yaowu & Zhu, Liping, 2022. "Independence tests in the presence of measurement errors: An invariance law," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    7. Zhou, Yeqing & Liu, Jingyuan & Zhu, Liping, 2020. "Test for conditional independence with application to conditional screening," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    8. Vakilifard, Negar & A. Bahri, Parisa & Anda, Martin & Ho, Goen, 2019. "An interactive planning model for sustainable urban water and energy supply," Applied Energy, Elsevier, vol. 235(C), pages 332-345.
    9. Lai, Tingyu & Zhang, Zhongzhan & Wang, Yafei & Kong, Linglong, 2021. "Testing independence of functional variables by angle covariance," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    10. Zhang, Qingyang, 2019. "Independence test for large sparse contingency tables based on distance correlation," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 17-22.
    11. Mordant, Gilles & Segers, Johan, 2022. "Measuring dependence between random vectors via optimal transport," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    12. Liu, Jicai & Si, Yuefeng & Niu, Yong & Zhang, Riquan, 2022. "Projection quantile correlation and its use in high-dimensional grouped variable screening," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    13. Cencheng Shen & Joshua T. Vogelstein, 2021. "The exact equivalence of distance and kernel methods in hypothesis testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 385-403, September.
    14. Hongjian Shi & Marc Hallin & Mathias Drton & Fang Han, 2020. "Rate-Optimality of Consistent Distribution-Free Tests of Independence Based on Center-Outward Ranks and Signs," Working Papers ECARES 2020-23, ULB -- Universite Libre de Bruxelles.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:oup:biomet:v:104:y:2017:i:4:p:829-843.. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.