Primordial non-Gaussianity:: local curvature method and statistical significance of constraints on fNL from WMAP data

We test the consistency of estimates of the non-linear coupling constant f(NL) using non-Gaussian cosmic microwave background (CMB) maps generated by the method described in the work of Liguori, Matarrese & Moscardini. This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on the estimation of f(NL). Nevertheless, using spherical wavelets, we find results in very good agreement with Mukherjee & Wang, 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(-260)(+270) at the 2 sigma level (Bayesian) and f(NL) = -10(-270)(+310) (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 the work of Cabella et al., the estimates may be combined to reduce the error bars. In this way, we obtain f(NL) = -5 +/- 85 and f(NL) = -5 +/- 175 at the 1 sigma and 2 sigma level respectively using the frequentist approach.