In this work we present constraints on different shapes of primordial
non-Gaussianity using the Wilkinson Microwave Anisotropy Probe (WMAP) 7-year
data and the spherical Mexican hat wavelet fnl estimator including the linear
term correction. In particular we focus on the local, equilateral and
orthogonal shapes. We first analyse the main statistical properties of the
wavelet estimator and show the conditions to reach optimality. We include the
linear term correction in our estimators and compare the estimates with the
values already published using only the cubic term. The estimators are tested
with realistic WMAP simulations with anisotropic noise and the WMAP KQ75 sky
cut. The inclusion of the linear term correction shows a negligible improvement
(< 1 per cent) in the error-bar for any of the shapes considered. The results
of this analysis show that, in the particular case of the wavelet estimator,
the optimality for WMAP anisotropy levels is basically achieved with the mean
subtraction and in practical terms there is no need of including a linear term
once the mean has been subtracted. Our best estimates are now: local fnl = 39.0
+/ 21.4, equilateral fnl = -62.8 +/- 154.0 and orthogonal fnl = -159.8 +/-
115.1 (all cases 68 per cent CL). We have also computed the expected linear
term correction for simulated Planck maps with anisotropic noise at 143 GHz
following the Planck Sky Model and including a mask. The improvement achieved
in this case for the local fnl error-bar is also negligible (0.4 per cent).Comment: 8 pages, 5 figures, 4 tables. Minor revision, one figure added,
accepted for publication in MNRA
