IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v150y2022icp280-322.html
   My bibliography  Save this article

Distance covariance for random fields

Author

Listed:
  • Matsui, Muneya
  • Mikosch, Thomas
  • Roozegar, Rasool
  • Tafakori, Laleh

Abstract

We study an independence test based on distance correlation for random fields (X,Y). We consider the situations when (X,Y) is observed on a lattice with equidistant grid sizes and when (X,Y) is observed at random locations. We provide asymptotic theory for the sample distance correlation in both situations and show bootstrap consistency. The latter fact allows one to build a test for independence of X and Y based on the considered discretizations of these fields. We illustrate the performance of the bootstrap test by simulations, and apply the test to Japanese meteorological data observed over the entire area of Japan.

Suggested Citation

  • Matsui, Muneya & Mikosch, Thomas & Roozegar, Rasool & Tafakori, Laleh, 2022. "Distance covariance for random fields," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 280-322.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:280-322
    DOI: 10.1016/j.spa.2022.04.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922000965
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.04.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2021. "Testing serial independence with functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 603-629, September.
    2. Zhou Zhou, 2012. "Measuring nonlinear dependence in time‐series, a distance correlation approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 438-457, May.
    3. K Fokianos & M Pitsillou, 2018. "Testing independence for multivariate time series via the auto-distance correlation matrix," Biometrika, Biometrika Trust, vol. 105(2), pages 337-352.
    4. Shih-Hao Huang & Hsin-Cheng Huang & Ruey S. Tsay & Guangming Pan, 2021. "Testing Independence Between Two Spatial Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(2), pages 161-179, June.
    5. Székely, Gábor J. & Rizzo, Maria L., 2013. "The distance correlation t-test of independence in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 193-213.
    6. Shun Yao & Xianyang Zhang & Xiaofeng Shao, 2018. "Testing mutual independence in high dimension via distance covariance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 455-480, June.
    7. Dehling, H. & Mikosch, T., 1994. "Random Quadratic Forms and the Bootstrap for U-Statistics," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 392-413, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chu, Ba, 2023. "A distance-based test of independence between two multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    2. Ivair R. Silva & Yan Zhuang & Julio C. A. da Silva Junior, 2022. "Kronecker delta method for testing independence between two vectors in high-dimension," Statistical Papers, Springer, vol. 63(2), pages 343-365, April.
    3. Marrel, Amandine & Chabridon, Vincent, 2021. "Statistical developments for target and conditional sensitivity analysis: Application on safety studies for nuclear reactor," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    4. Simos G. Meintanis & Joseph Ngatchou-Wandji & James Allison, 2018. "Testing for serial independence in vector autoregressive models," Statistical Papers, Springer, vol. 59(4), pages 1379-1410, December.
    5. Tarik Bahraoui & Jean‐François Quessy, 2022. "Tests of multivariate copula exchangeability based on Lévy measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1215-1243, September.
    6. Yongshuai Chen & Wenwen Guo & Hengjian Cui, 2024. "On the test of covariance between two high-dimensional random vectors," Statistical Papers, Springer, vol. 65(5), pages 2687-2717, July.
    7. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2017. "Distance correlation coefficients for Lancaster distributions," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 19-39.
    8. Shang, Du & Shang, Pengjian, 2022. "The dependence measurements based on martingale difference correlation and distance correlation: Efficient tools to distinguish different complex systems," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    9. 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.
    10. Jin, Ze & Matteson, David S., 2018. "Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 304-322.
    11. Dueck, Johannes & Edelmann, Dominic & Richards, Donald, 2015. "A generalization of an integral arising in the theory of distance correlation," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 116-119.
    12. Guochang Wang & Wai Keung Li & Ke Zhu, 2018. "New HSIC-based tests for independence between two stationary multivariate time series," Papers 1804.09866, arXiv.org.
    13. Wan, Phyllis & Davis, Richard A., 2022. "Goodness-of-fit testing for time series models via distance covariance," Journal of Econometrics, Elsevier, vol. 227(1), pages 4-24.
    14. Rauf Ahmad, M., 2019. "A significance test of the RV coefficient in high dimensions," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 116-130.
    15. Dominic Edelmann & Tobias Terzer & Donald Richards, 2021. "A Basic Treatment of the Distance Covariance," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 12-25, May.
    16. Meintanis, S.G. & Milošević, B. & Jiménez–Gamero, M.D., 2024. "Goodness–of–fit tests based on the min–characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).
    17. Zhang, Qingyang, 2019. "Independence test for large sparse contingency tables based on distance correlation," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 17-22.
    18. Jiménez-Gamero, M. Dolores & Kim, Hyoung-Moon, 2015. "Fast goodness-of-fit tests based on the characteristic function," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 172-191.
    19. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    20. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).

    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:eee:spapps:v:150:y:2022:i:c:p:280-322. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.