A. Curto, E. Martinez-Gonzalez, R. B. Barreiro
We present a comprehensive study of the wavelet estimator to detect
primordial non-Gaussianity in Cosmic Microwave Background data. We first
summarise the main assumptions made to derive the estimator based on the direct
bispectrum in harmonic space. We then analyse the main statistical properties
of the wavelet estimator and show the conditions to reach optimality. In
particular, we clarify some points regarding the spherical Mexican hat wavelet
fnl estimator and the recent issue raised about the need to introduce a linear
term to achieve optimality. We define the likelihood for the fnl parameter in
terms of the cubic statistics constructed from the wavelet coefficient maps. We
compute the fnl estimator from the previous likelihood. The analytical results
obtained are checked with simulations containing different degrees of
complexity, including anisotropic noise. The results of this analysis show
that, in the particular case of this estimator, the optimality is achieved
without the need of including a linear term. For illustration we analyse
simulated CMB maps with resolution and noise level matching those of the WMAP
V+W 7-year.
View original:
http://arxiv.org/abs/1111.3390
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