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

Leonenko, Nikolai, Taqqu, Murad S. and Terdik, Gyorgy H. 2018. Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem. Electronic Journal of Statistics 12 (2) , pp. 3114-3146. 10.1214/18-EJS1473

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Abstract

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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: Institute of Mathematical Statistics
ISSN: 1935-7524
Date of First Compliant Deposit: 28 August 2018
Date of Acceptance: 27 August 2018
Last Modified: 28 Jun 2019 05:10
URI: http://orca.cf.ac.uk/id/eprint/114399

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