On The Dependence Structure of Wavelet Coefficients for Spherical Random Fields

Details On The Dependence Structure of Wavelet Coefficients for Spherical Random Fields On The Dependence Structure of Wavelet Coefficients for Spherical Random Fields

2008-05-27

arxiv.org/abs/0805.4154v2

Stochastic Processes and their Applications, Vol. 119 (2009), pp. 3749-3766

Mathematics

Statistics Theory

Revised version for Stochastic Processes and their Applications

Scientific paper

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.

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