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We study the weak convergence (in the high-frequency limit) of the parameterestimators of power spectrum coefficients associated with Gaussian, sphericaland isotropic random fields. In particular, we introduce a Whittle-typeapproximate maximum likelihood estimator and we investigate its asympotic weakconsistency and Gaussianity, in both parametric and semiparametric cases.

Gaussian semiparametric estimates on the unit sphere