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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1537841410

Digital Object Identifier
doi:10.1214/18-EJS1473

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

Keywords
Astronomy cosmic variance Laplace-Beltrami model Rosenblatt distribution

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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