Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem
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Published version
Date
2018
Authors
Taqqu, Murad S.
Leonenko, Nikolai N.
Terdik, Gyorgy
Version
Published version
OA Version
Citation
M. Taqqu, Nikolai N Leonenko, Gyorgy Terdik. "Estimation of the Covariance Function of Gaussian Isotropic Random Fields on Spheres, related Rosenblatt-type Distributions and the Cosmic Variance Problem." Electron. J. Statist., Volume 12, Number 2 (2018), 3114-3146. https://doi.org/10.1214/18-EJS1473
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.
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Attribution-NonCommercial-NoDerivatives 4.0 International