Journal
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
Volume 34, Issue 5, Pages 723-732Publisher
SPRINGER
DOI: 10.1007/s00477-020-01796-y
Keywords
Axial symmetry; Covariance function; Fourier inversion; Reducibility
Categories
Funding
- CONICYT/FONDECYT/REGULAR [1170290]
- FAPESP [2016/09906-0]
- CNPq [203033/2019-1]
Ask authors/readers for more resources
Axial symmetry for covariance functions defined over spheres has been a very popular assumption for climate, atmospheric, and environmental modeling. For Gaussian random fields defined over spheres embedded in a three-dimensional Euclidean space, maximum likelihood estimation techiques as well kriging interpolation rely on the inverse of the covariance matrix. For any collection of points where data are observed, the covariance matrix is determined through the realizations of the covariance function associated with the underlying Gaussian random field. If the covariance function is not strictly positive definite, then the associated covariance matrix might be singular. We provide conditions for strict positive definiteness of any axially symmetric covariance function. Furthermore, we find conditions for reducibility of an axially symmetric covariance function into a geodesically isotropic covariance. Finally, we provide conditions that legitimate Fourier inversion in the series expansion associated with an axially symmetric covariance function.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available