Needlet-Whittle Estimates on the Unit Sphere

TL;DR

This paper analyzes the asymptotic properties of needlet-based estimators for spectral parameters of spherical random fields, demonstrating their consistency and Gaussianity at high frequencies, with supporting Monte Carlo simulations.

Contribution

It extends previous Fourier-based results by establishing asymptotic properties of needlet-based estimators on the sphere.

Findings

Proves consistency of needlet-Whittle estimators.

Establishes asymptotic Gaussianity in high-frequency limit.

Supports theoretical results with Monte Carlo simulations.

Abstract

We study the asymptotic behaviour of needlets-based approximate maximum likelihood estimators for the spectral parameters of Gaussian and isotropic spherical random fields. We prove consistency and asymptotic Gaussianity, in the high-frequency limit, thus generalizing earlier results by Durastanti et al. (2011) based upon standard Fourier analysis on the sphere. The asymptotic results are then illustrated by an extensive Monte Carlo study.