DO WAVELETS REALLY DETECT NON-GAUSSIANITY IN THE 4-YEAR COBE DATA ?
M.P. HOBSON, P. MUKHERJEE & A.N. LASENBY
We investigate the detection of non-Gaussianity in the 4-year COBE DMR-DSMB data reported by Pando, Valls-Gabaud & Fang (1998), using a technique based on the discrete wavelet transform. The analysis is performed on the two DMR faces centred on the North and South Galactic poles respectively, using the Daubechies 4 wavelet basis. We show that the results depend critically on the orientation of the data, and so should be treated with caution. For two distinct orientations, we calculate unbiased estimates of the skewness, kurtosis and scale-scale correlation of the corresponding wavelet coefficients in all of the available scale domains of the transform. We obtain several detections of non-Gaussianity at greater than the 99 per cent confidence level, but most of these occur on pixel-pixel scales and are therefore not cosmological in origin. Indeed, after removing all multipoles beyond $\ell = 40$ from the maps, only one robust detection remains. Moreover, using Monte-Carlo simulations, we find that the probability of obtaining such a detection by chance is 0.59. Thus, we conclude the wavelet technique does {\em not} yield strong evidence for non-Gaussianity of cosmological origin in the 4-year COBE DMR-DSMB data.