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Intrinsic random functions and universal kriging on the circle

Author

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  • Huang, Chunfeng
  • Zhang, Haimeng
  • Robeson, Scott M.

Abstract

Intrinsic random functions (IRF) provide a versatile approach when the assumption of second-order stationarity is not met. Here, we develop the IRF theory on the circle with its universal kriging application. Unlike IRF in Euclidean spaces, where differential operations are used to achieve stationarity, our result shows that low-frequency truncation of the Fourier series representation of the IRF is required for such processes on the circle. All of these features and developments are presented through the theory of reproducing kernel Hilbert space. In addition, the connection between kriging and splines is also established, demonstrating their equivalence on the circle.

Suggested Citation

  • Huang, Chunfeng & Zhang, Haimeng & Robeson, Scott M., 2016. "Intrinsic random functions and universal kriging on the circle," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 33-39.
    • Handle: RePEc:eee:stapro:v:108:y:2016:i:c:p:33-39
    DOI: 10.1016/j.spl.2015.09.023
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    References listed on IDEAS

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    1. Wood, Andrew T. A., 1995. "When is a truncated covariance function on the line a covariance function on the circle?," Statistics & Probability Letters, Elsevier, vol. 24(2), pages 157-164, August.
    2. Dufour, Jean-Marie & Roy, Roch, 1976. "On spectral estimation for a homogeneous random process on the circle," Stochastic Processes and their Applications, Elsevier, vol. 4(2), pages 107-120, April.
    3. Gneiting, Tilmann, 1998. "Simple tests for the validity of correlation function models on the circle," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 119-122, August.
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    Cited by:

    1. Huang, Chunfeng & Li, Ao, 2021. "On Lévy’s Brownian motion and white noise space on the circle," Statistics & Probability Letters, Elsevier, vol. 171(C).
    2. Huang, Chunfeng & Zhang, Haimeng & Robeson, Scott M. & Shields, Jacob, 2019. "Intrinsic random functions on the sphere," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 7-14.

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