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

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, 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:	07 Nov 2023 00:49
URI:	https://orca.cardiff.ac.uk/id/eprint/114399

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