On The Dependence Structure of Wavelet Coefficients for Spherical Random Fields
arXiv:0805.4154
Abstract
We consider the correlation structure of the random coefficients for a wide class of wavelet systems on the sphere (Mexican needlets) which were recently introduced in the literature by Geller and Mayeli (2007). We provide necessary and sufficient conditions for these coefficients to be asymptotic uncorrelated in the real and in the frequency domain. Here, the asymptotic theory is developed in the high resolution sense. Statistical applications are also discussed, in particular with reference to the analysis of cosmological data.
Revised version for Stochastic Processes and their Applications
References in corpus (6)
- A full sky, low foreground, high resolution CMB map from WMAP
- An Estimate of the Primordial Non-Gaussianity Parameter f_NL Using the Needlet Bispectrum from WMAP
- Cosmological applications of a wavelet analysis on the sphere
- Consistency of a needlet spectral estimator on the sphere
- Asymptotic Uncorrelation for Mexican Needlets
- Nearly Tight Frames and Space-Frequency Analysis on Compact Manifolds