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We study the statistical properties of the 1st year WMAP data on differentscales using the spherical mexican hat wavelet transform. Consistent with theresults of Vielva et al. (2003) we find a deviation from Gaussianity in theform of kurtosis of wavelet coefficients on $3-4^\circ$ scales in the southernGalactic hemisphere. This paper extends the work of Vielva et al. as follows.We find that the non-Gaussian signal shows up more strongly in the form of alarger than expected number of cold pixels and also in the form of scale-scalecorrelations amongst wavelet coefficients. We establish the robustness of thenon-Gaussian signal under more wide-ranging assumptions regarding the Galacticmask applied to the data and the noise statistics. This signal is unlikely tobe due to the usual quadratic term parametrized by the non-linearity parameter$f_{NL}$. We use the skewness of the spherical mexican hat wavelet coefficientsto constrain $f_{NL}$ with the 1st year WMAP data. Our results constrain$f_{NL}$ to be $50\pm 80$ at 68% confidence, and less than 280 at 99%confidence.Comment: 22 pages, 10 figures, ApJ accepte

Wavelets andWilkinson Microwave Anisotropy ProbeNon‐Gaussianity