Locally Anisotropic Nonstationary Covariance Functions on the Sphere

Jian Cao, Jingjie Zhang, Zhuoer Sun and Matthias Katzfuss ()
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Jian Cao: Texas A &M University
Jingjie Zhang: Texas A &M University
Zhuoer Sun: Texas A &M University
Matthias Katzfuss: Texas A &M University

Journal of Agricultural, Biological and Environmental Statistics, 2024, vol. 29, issue 2, No 2, 212-231

Abstract: Abstract Rapid developments in satellite remote-sensing technology have enabled the collection of geospatial data on a global scale, hence increasing the need for covariance functions that can capture spatial dependence on spherical domains. We propose a general method of constructing nonstationary, locally anisotropic covariance functions on the sphere based on covariance functions in $$\mathbb {R}^3$$ R 3 . We also provide theorems that specify the conditions under which the resulting correlation function is isotropic or axially symmetric. For large datasets on the sphere commonly seen in modern applications, the Vecchia approximation is used to achieve higher scalability on statistical inference. The importance of flexible covariance structures is demonstrated numerically using simulated data and a precipitation dataset. Supplementary materials accompanying this paper appear online.

Keywords: Axial symmetry; Local anisotropy; Nonstationarity; Global data; Vecchia approximation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13253-023-00573-y

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