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    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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    License
    Attribution-NonCommercial-NoDerivatives 4.0 International
    Date Issued
    2018
    Publisher Version
    10.1214/18-EJS1473
    Author(s)
    Taqqu, Murad S.
    Leonenko, Nikolai N.
    Terdik, Gyorgy
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    Permanent Link
    https://hdl.handle.net/2144/37513
    Version
    Published version
    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
    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
    Collections
    • CAS: Mathematics & Statistics: Scholarly Papers [266]
    • BU Open Access Articles [3727]


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