Spin Needlets Spectral Estimation

TL;DR

This paper develops statistical methods using spin needlets for estimating the spectral properties of spin fields on the sphere, with applications to cosmological polarization data, addressing noise and missing data issues.

Contribution

It introduces a spectral estimation technique based on spin needlets for spin fields, including CLT results and tests for bias and asymmetries, advancing analysis tools for cosmological data.

Findings

Central Limit Theorem for spin needlet spectral estimates

Effective handling of noise and missing data in spectral estimation

Tests for bias and asymmetries with asymptotic justification

Abstract

We consider the statistical analysis of random sections of a spin fibre bundle over the sphere. These may be thought of as random fields that at each point p in $S^2$ take as a value a curve (e.g. an ellipse) living in the tangent plane at that point $T_{p}S^2$, rather than a number as in ordinary situations. The analysis of such fields is strongly motivated by applications, for instance polarization experiments in Cosmology. To investigate such fields, spin needlets were recently introduced by Geller and Marinucci (2008) and Geller et al. (2008). We consider the use of spin needlets for spin angular power spectrum estimation, in the presence of noise and missing observations, and we provide Central Limit Theorem results, in the high frequency sense; we discuss also tests for bias and asymmetries with an asymptotic justification.