On the optimality of the spherical Mexican hat wavelet estimator for the primordial non-Gaussianity

We study the spherical Mexican hat wavelet 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 f(nl) 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 f(nl), that is, the variance of this parameter Sigma 2(f(nl)), and compare it with the variance obtained from the primary bispectrum for the same experiment. Finally, we apply our wavelet-based estimator on Wilkinson Microwave Anisotropy Probe 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.