分野別セミナー

Estimating the covariance function of a Gaussian isotropic random field on the unit sphere of the 3D Euclidean space has primary importance. We assume that an observation is given and consider an estimator of the covariance function. We show that this estimator follows a Rosenblatt type distribution. The asymptotic distribution of the truncated version of the estimator is also given. One can substitute the usual estimator of the spectrum by estimating the covariance function first then using the Gauss-Legendre quadrature for estimation of the spectrum. The problem of cosmic variance is also considered. In practice the observations are given on a high resolution discretized sphere (for instance the Cosmic Microwave Background (CMB) data).


This is a joint work with M. S. Taqqu (Boston University, USA) and Gy. Terdik (University of Debrecen, Hungary).