Subsampling needlet coefficients on the sphere

TL;DR

This paper develops a subsampling method for needlet coefficients on the sphere, enabling statistical inference like isotropy testing and bootstrap estimation from a single spherical data realization.

Contribution

It introduces a novel subsampling approach based on needlet coefficients' asymptotic uncorrelation for spherical data analysis.

Findings

Effective isotropy tests demonstrated

Bootstrap estimation of nuisance parameters feasible

Method applicable with a single data realization

Abstract

In a recent paper, we analyzed the properties of a new kind of spherical wavelets (called needlets) for statistical inference procedures on spherical random fields; the investigation was mainly motivated by applications to cosmological data. In the present work, we exploit the asymptotic uncorrelation of random needlet coefficients at fixed angular distances to construct subsampling statistics evaluated on Voronoi cells on the sphere. We illustrate how such statistics can be used for isotropy tests and for bootstrap estimation of nuisance parameters, even when a single realization of the spherical random field is observed. The asymptotic theory is developed in detail in the high resolution sense.