Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem
Taqqu, Murad S.
Leonenko, Nikolai N.
MetadataShow full item record
Citation (published version)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
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.
RightsAttribution-NonCommercial-NoDerivatives 4.0 International