Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Cosmological Non-Gaussian Signature Detection: Comparing Performance of Different Statistical Tests | EURASIP Journal on Applied Signal Processing 2005 15 2470-2485 2005 Hindawi Publishing Corporation Cosmological Non-Gaussian Signature Detection Comparing Performance of Different Statistical Tests J. Jin Department of Statistics Purdue University 150 N. University Street West Lafayette IN 47907 USA Email jinj@ . Starck DAPNIA SEDI-SAP Service d Astrophysique CEA-Saclay 91191 Gif-sur-Yvette Cedex France Email jstarck@ D. L. Donoho Department of Statistics Stanford University Sequoia Hall Stanford CA 94305 USA Email donoho@ N. Aghanim IAS-CNRS Universite Paris Sud Batiment 121 91405 Orsay Cedex France Email aghanim@ Division of Theoretical Astronomy National Astronomical Observatory of Japan Osawa 2-21-1 Mitaka Tokyo 181-8588 Japan O. Forni IAS-CNRS Universite Paris Sud Batiment 121 91405 Orsay Cedex France Email Received 30 June 2004 Currently it appears that the best method for non-Gaussianity detection in the cosmic microwave background CMB consists in calculating the kurtosis of the wavelet coefficients. We know that wavelet-kurtosis outperforms other methods such as the bispectrum the genus ridgelet-kurtosis and curvelet-kurtosis on an empirical basis but relatively few studies have compared other transform-based statistics such as extreme values or more recent tools such as higher criticism HC or proposed best possible choices for such statistics. In this paper we consider two models for transform-domain coefficients a a power-law model which seems suited to the wavelet coefficients of simulated cosmic strings and b a sparse mixture model which seems suitable for the curvelet coefficients of filamentary structure. For model a if power-law behavior holds with finite 8th moment excess kurtosis is an asymptotically optimal detector but if the 8th moment is not finite a test based on extreme values is asymptotically optimal. For model b if the transform coefficients are very sparse a recent test
