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A simplified representation of the covariance structure of axially symmetric processes on the sphere

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

Abstract

Spatial processes having covariance functions that depend solely on the distance between locations are known as homogeneous. Many random processes on the sphere are not homogeneous, especially in the latitudinal dimension. As a result, we study a class of statistical processes that exhibit axial symmetry, whereby their covariance function depends on differences in longitude alone. We develop a new and simplified representation for a valid axially symmetric process, reducing computational complexity considerably. In addition, we explore longitudinally reversible processes and the construction of parametric models for axially symmetric processes.

Suggested Citation

  • Huang, Chunfeng & Zhang, Haimeng & Robeson, Scott M., 2012. "A simplified representation of the covariance structure of axially symmetric processes on the sphere," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1346-1351.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:7:p:1346-1351
    DOI: 10.1016/j.spl.2012.03.015
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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. 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.
    3. Ta-Hsin Li & Gerald North, 1997. "Aliasing Effects and Sampling Theorems of Spherical Random Fields when Sampled on a Finite Grid," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 341-354, June.
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    Cited by:

    1. Arafat, Ahmed & Porcu, Emilio & Bevilacqua, Moreno & Mateu, Jorge, 2018. "Equivalence and orthogonality of Gaussian measures on spheres," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 306-318.
    2. Lan, Xiaohong & Xiao, Yimin, 2018. "Strong local nondeterminism of spherical fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 44-50.
    3. Stefano Castruccio & Joseph Guinness, 2017. "An evolutionary spectrum approach to incorporate large-scale geographical descriptors on global processes," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 329-344, February.
    4. 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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