Isotropic covariance functions on spheres: Some properties and modeling considerations

Introducing flexible covariance functions is critical for interpolating spatial data since the properties of interpolated surfaces depend on the covariance function used for Kriging. An extensive literature is devoted to covariance functions on Euclidean spaces, where the Mat´ern covariance family is a valid and flexible parametric family capable of controlling the smoothness of corresponding stochastic processes. Many applications in environmental statistics involve data located on spheres, where less is known about properties of covariance functions, and where the Mat´ern is not generally a valid model with great circle distance metric. In this paper, we advance the understanding of covariance functions on spheres by defining the notion of and proving a characterization theorem for m times mean square differentiable processes on d-dimensional spheres. Stochastic processes on spheres are commonly constructed by restricting processes on Euclidean spaces to spheres of lower dimen...

• Type: Journal
• Year: 2016
• Where: MA
• Authors: Joseph Guinness, Montserrat Fuentes
• Keywords: Communications, MA 2016