  We test the consistency of estimates of the non-linear coupling constant
f_{NL} using non-Gaussian CMB maps generated by the method described in
(Liguori, Matarrese and Moscardini 2003). This procedure to obtain non-Gaussian
maps differs significantly from the method used in previous works on estimation
of f_{NL}. Nevertheless, using spherical wavelets, we find results in very good
agreement with (Mukherjee and Wang 2004), showing that the two ways of
generating primordial non-Gaussian maps give equivalent results. Moreover, we
introduce a new method for estimating the non-linear coupling constant from CMB
observations by using the local curvature of the temperature fluctuation field.
We present both Bayesian credible regions (assuming a flat prior) and proper
(frequentist) confidence intervals on f_{NL}, and discuss the relation between
the two approaches. The Bayesian approach tends to yield lower error bars than
the frequentist approach, suggesting that a careful analysis of the different
interpretations is needed. Using this method, we estimate
f_{NL}=-10^{+270}_{-260} at the 2\sigma level (Bayesian) and
f_{NL}=-10^{+310}_{-270} (frequentist). Moreover, we find that the wavelet and
the local curvature approaches, which provide similar error bars, yield
approximately uncorrelated estimates of f_{NL} and therefore, as advocated in
(Cabella et al. 2004), the estimates may be combined to reduce the error bars.
In this way, we obtain f_{NL}=-5\pm 85 and f_{NL}=-5\pm 175 at the 1\sigma and
2\sigma level respectively using the frequentist approach.
