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

Files
euclid.ejs.1537841410.pdf(1.05 MB)
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.
Description
License
Attribution-NonCommercial-NoDerivatives 4.0 International