Gaussian semiparametric estimates on the unit sphere

TL;DR

This paper investigates the asymptotic behavior of estimators for power spectrum coefficients of Gaussian, isotropic spherical random fields, introducing a Whittle-type estimator and analyzing its consistency and distribution in high-frequency limits.

Contribution

It introduces a new Whittle-type estimator for power spectrum coefficients and studies its asymptotic properties in both parametric and semiparametric settings.

Findings

Estimator is asymptotically consistent.

Estimator exhibits Gaussian asymptotic distribution.

Results apply to high-frequency limits of spherical random fields.

Abstract

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