Higher Criticism Statistic: Detecting and Identifying Non-Gaussianity in the WMAP First Year Data

Higher Criticism is a recently developed statistic for non-Gaussian detection, proposed in Donoho & Jin 2004, where it has been shown to be effective at resolving a very subtle testing problem: whether n normal means are all zero versus the alternative that a small fraction is nonzero. Higher Criticism is also useful in the detection of a non-Gaussian convolution component of cosmic strings in the Cosmic Microwave Background (CMB), see Jin et al. 2004. In this paper, we study how well the anisotropies of the CMB fit with the homogeneous and isotropic Gaussian distribution predicted by the Standard Inflationary model. We find that Higher Criticism is useful for two purposes. First, Higher Criticism has competitive detection power, and non-Gaussianity is detected at the level 99% in the first year WMAP data. We generated 5000 Monte Carlo Gaussian simulations of the CMB maps. By applying the Higher Criticism to all of these maps in wavelet space, we constructed confidence regions of Higher Criticism at levels 68%, 95%, and 99%. We find that the Higher Criticism value of WMAP is outside the 99% confidence region at a wavelet scale of 5 degrees (99.46% of Higher Criticism values based on simulated maps are below the values for WMAP). Second, Higher Criticism offers a way to locate a small portion of data that accounts for the nonGaussianity. This property is not immediately available for other statistical tests such as the widely-used excess kurtosis test. Using Higher Criticism, we have successfully identified a ring of pixels centered at (l ≈ 209◦, b ≈ −57◦), which seems to account for the observed detection of non-Gaussianity