On the linear term correction for needlets/wavelets non-Gaussianity estimators

We derive the linear correction term for needlet and wavelet estimators of the bispectrum and the non-linearity parameter fNL on cosmic microwave background radiation data. We show that on masked WMAP-like data with anisotropic noise, the error bars improve by 10-20% and almost reach the optimal error bars obtained with the KSW estimator (Komatsu et al 2005). In the limit of full-sky and isotropic noise, this term vanishes. We apply needlet and wavelet estimators to the WMAP 7-year data and obtain our best estimate fNL=37.5 \pm 21.8.