Goodness-of-Fit Tests to study the Gaussianity of the MAXIMA data

Abstract

Goodness-of-Fit tests, including Smooth ones, are introduced and applied to detect non-Gaussianity in Cosmic Microwave Background simulations. We study the power of three different tests: the Shapiro-Francia test (1972), the uncategorised smooth test developed by Rayner and Best(1990) and the Neyman's Smooth Goodness-of-fit test for composite hypotheses (Thomas and Pierce 1979). The Smooth Goodness-of-Fit tests are designed to be sensitive to the presence of ``smooth'' deviations from a given distribution. We study the power of these tests based on the discrimination between Gaussian and non-Gaussian simulations. Non-Gaussian cases are simulated using the Edgeworth expansion and assuming pixel-to-pixel independence. Results show these tests behave similarly and are more powerful than tests directly based on cumulants of order 3, 4, 5 and 6. We have applied these tests to the released MAXIMA data. The applied tests are built to be powerful against detecting deviations from univariate Gaussianity. The Cholesky matrix corresponding to signal (based on an assumed cosmological model) plus noise is used to decorrelate the observations previous to the analysis. Results indicate that the MAXIMA data are compatible with Gaussianity.

arXiv commentMNRAS, in press

References in corpus (16)

• Acoustic Signatures in the Primary Microwave Background Bispectrum
• The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
• Non-Gaussianity in multi-field inflation
• Non-Gaussianity from Inflation
• Measurement of the cosmic microwave background bispectrum on the COBE DMR sky maps
• The performance of spherical wavelets to detect non-Gaussianity in the CMB sky
• Non-Gaussian Signatures in the Cosmic Background Radiation from Warm Inflation
• An Isocurvature CDM Cosmogony. II. Observational Tests
• Tests for Gaussianity of the MAXIMA-1 CMB Map
• An Isocurvature CDM Cosmogony. I. A Worked Example of Evolution Through Inflation
• Is the cosmic microwave background really non-Gaussian?
• Estimate of the Cosmological Bispectrum from the MAXIMA-1 Cosmic Microwave Background Map
• Multiple Methods for Estimating the Bispectrum of the Cosmic Microwave Background with Application to the MAXIMA Data
• COBE-DMR constraints on the nonlinear coupling parameter: a wavelet based method
• Boomerang returns unexpectedly
• Fluctuations in the CMB Induced by Cosmic Strings: Methods and Formalism

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• Data analysis methods for the cosmic microwave background
• Testing Gaussianity on Archeops Data
• On the optimality of the spherical Mexican hat wavelet estimator for the primordial non-Gaussianity
• Effect of component separation on the temperature distribution of the CMB
• Gaussianity of the CMB: Smooth Goodness of Fit Tests Applied to Interferometric Data
• Tests of Gaussianity
• Cosmic Microwave Background anisotropies: the power spectrum and beyond