On the dependence structure of wavelet coefficients for spherical random fields

Abstract

We consider the correlation structure of the random coefficients for a class of wavelet systems on the sphere (labelled Mexican needlets) which was recently introduced in the literature by [D. Geller, A. Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Preprint, 2007. arxiv:0706.3642v2]. We provide necessary and sufficient conditions for these coefficients to be asymptotically uncorrelated in the real and in the frequency domain. Here, the asymptotic theory is developed in the high frequency sense. Statistical applications are also discussed, in particular with reference to the analysis of cosmological data. (C) 2009 Elsevier B.V. All rights reserved

Asymptotic uncorrelation for Mexican needlets

“…(12) Now let N be the least integer larger than μ/2 + 1. The equality (12) implies l a N l Z l (cos θ) c l (2l + 1)l −2N+μ C .…”

Spin Wavelets on the Sphere

“…Spherical needlets were recently introduced by [38,39], and further developed, and extended to general smooth compact Riemannian manifolds in [18][19][20]. In a random fields environment, needlets were investigated by [5,6], with a view to applications to the statistical analysis of CMB data; applications in the physical literature include [26,34,42], see also [12,15,16,30] and [31,35].…”

Spectral estimation on the sphere with needlets: high frequency asymptotics

“…Remark 3 A generalization of this B-adic framework, in a different direction to the one of Guilloux et al (2009) can be found in Geller andMayeli (2009), Mayeli (2010), Lan and Marinucci (2009). The authors do not suppose that the function a (or b) is compactly supported and obtain localization and asymptotic uncorrelation results similar to Propositions 3 and 4.…”