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Distance covariance for random fields

Author

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  • 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
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    References listed on IDEAS

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    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.
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