Electronic Journal of Statistics

Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem

Nikolai N. Leonenko, Murad S. Taqqu, and Gyorgy H. Terdik

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We consider the problem of estimating the covariance function of an isotropic Gaussian stochastic field on the unit sphere using a single observation at each point of the discretized sphere. The spatial estimator of the covariance function is expressed in a new form which provides, on one hand a way to derive the characteristic function of the estimator, and on the other hand a computationally efficient method to do so. We also describe a methodology for handling the presence of the cosmic variance which can impair the results. In simulation, we use the pixelization scheme HEALPix.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 3114-3146.

Received: July 2017
First available in Project Euclid: 25 September 2018

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Digital Object Identifier

Primary: 62M30: Spatial processes 60G60: Random fields
Secondary: 60F05: Central limit and other weak theorems

Astronomy cosmic variance Laplace-Beltrami model Rosenblatt distribution

Creative Commons Attribution 4.0 International License.


Leonenko, Nikolai N.; Taqqu, Murad S.; Terdik, Gyorgy H. Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem. Electron. J. Statist. 12 (2018), no. 2, 3114--3146. doi:10.1214/18-EJS1473. https://projecteuclid.org/euclid.ejs/1537841410

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