Taqqu, Murad S.Leonenko, Nikolai N.Terdik, Gyorgy2019-08-292019-08-292018M. 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-EJS1473https://hdl.handle.net/2144/37513We 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.Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Statistics & probabilityMathematicsAstronomyCosmic varianceLaplace-Beltrami modelRosenblatt distributionStatisticsArticle10.1214/18-EJS14730000-0002-1145-9082 (Taqqu, M)389166