The needlets bispectrum

TL;DR

This paper introduces the needlets bispectrum, a new statistical tool for analyzing non-Gaussian features in spherical data like Cosmic Microwave Background radiation, combining wavelet and higher-order spectral analysis.

Contribution

It develops the theoretical foundation and convergence results for the needlets bispectrum, bridging wavelet analysis and higher-order spectral methods on the sphere.

Findings

Derived convergence results for the needlets bispectrum

Established its applicability for non-Gaussianity detection in CMB data

Provided a high-resolution limit theory

Abstract

The purpose of this paper is to join two different threads of the recent literature on random fields on the sphere, namely the statistical analysis of higher order angular power spectra on one hand, and the construction of second-generation wavelets on the sphere on the other. To this aim, we introduce the needlets bispectrum and we derive a number of convergence results. Here, the limit theory is developed in the high resolution sense. The leading motivation of these results is the need for statistical procedures for searching non-Gaussianity in Cosmic Microwave Background radiation.