DO WAVELETS REALLY DETECT NON-GAUSSIANITY IN THE 4-YEAR COBE DATA ?
M.P. HOBSON, P. MUKHERJEE & A.N. LASENBY
Astrophysics Group, Cavendish Laboratory, Madingley Road,
Cambridge CB3 0HE, England
Abstract:
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.