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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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    5. 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.
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