On the optimality of the spherical Mexican hat wavelet estimator for the
  primordial non-Gaussianity
  We study the spherical Mexican hat wavelet (SMHW) as a detector of primordial
non-Gaussianity of the local type on the Cosmic Microwave Background (CMB)
anisotropies. For this purpose we define third order statistics based on the
wavelet coefficient maps and the original map. We find the dependence of these
statistics in terms of the non-linear coupling parameter fnl and the bispectrum
of this type of non-Gaussianity. We compare the analytical values for these
statistics with the results obtained with non-Gaussian simulations for an ideal
full-sky CMB experiment without noise. We study the power of this method to
detect fnl, i. e. the variance of this parameter, and compare it with the
variance obtained from the primary bispectrum for the same experiment. Finally
we apply our wavelet based estimator on WMAP-like maps with incomplete sky and
inhomogeneous noise and compare with the optimal bispectrum estimator. The
results show that the wavelet cubic statistics are as efficient as the
bispectrum as optimal detectors of this type of primordial non-Gaussianity.
