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Testing Independence Between Two Spatial Random Fields

Author

Listed:
  • Shih-Hao Huang

    (National Central University)

  • Hsin-Cheng Huang

    (Academia Sinica)

  • Ruey S. Tsay

    (University of Chicago)

  • Guangming Pan

    (Nanyang Technological University)

Abstract

In this article, we consider testing independence between two spatial Gaussian random fields evaluated, respectively, at p and q locations with sample size n, where both p and q are allowed to be larger than n. We impose no spatial stationarity and no parametric structure for the two random fields. Our approach is based on canonical correlation analysis (CCA). But instead of applying CCA directly to the two random fields, which is not feasible for high-dimensional testing considered, we adopt a dimension-reduction approach using a special class of multiresolution spline basis functions. These functions are ordered in terms of their degrees of smoothness. By projecting the data to the function space spanned by a few leading basis functions, the spatial variation of the data can be effectively preserved. The test statistic is constructed from the first sample canonical correlation coefficient in the projected space and is shown to have an asymptotic Tracy–Widom distribution under the null hypothesis. Our proposed method automatically detects the signal between the two random fields and is designed to handle irregularly spaced data directly. In addition, we show that our test is consistent under mild conditions and provide three simulation experiments to demonstrate its powers. Moreover, we apply our method to investigate whether the precipitation in continental East Africa is related to the sea surface temperature (SST) in the Indian Ocean and whether the precipitation in west Australia is related to the SST in the North Atlantic Ocean.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:jagbes:v:26:y:2021:i:2:d:10.1007_s13253-020-00421-3
    DOI: 10.1007/s13253-020-00421-3
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    References listed on IDEAS

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    1. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
    2. Leo Breiman & Jerome H. Friedman, 1997. "Predicting Multivariate Responses in Multiple Linear Regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 3-54.
    3. Noel Cressie & Gardar Johannesson, 2008. "Fixed rank kriging for very large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 209-226, February.
    4. Joshua Hewitt & Jennifer A. Hoeting & James M. Done & Erin Towler, 2018. "Remote effects spatial process models for modeling teleconnections," Environmetrics, John Wiley & Sons, Ltd., vol. 29(8), December.
    5. Wen‐Ting Wang & Hsin‐Cheng Huang, 2018. "Regularized spatial maximum covariance analysis," Environmetrics, John Wiley & Sons, Ltd., vol. 29(2), March.
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    Cited by:

    1. 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.

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