Tests of Gaussianity

Aliaga, A. M.; Martínez-González, E.; Cayón, L.; Argüeso, F.; Sanz, J. L.; Barreiro, R. B.; Gallegos, J.

doi:10.1016/j.newar.2003.09.004

Cited by 6 publications

(12 citation statements)

References 15 publications

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“…In both cases a comparison with Gaussian predictions confirmed the compatibility of the MAXIMA data with Gaussianity. We have added three more tests to those applied to MAXIMA (also see Aliaga et. al.…”

Section: Discussionmentioning

confidence: 99%

Goodness-of-fit tests to study the Gaussianity of the MAXIMA data

Cayón¹,

Argüeso²,

Martínez-González³

et al. 2003

Monthly Notices RAS

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Goodness‐of‐fit tests, including smooth ones, are introduced and applied to detecting non‐Gaussianity in cosmic microwave background simulations. We study the power of three different tests: the Shapiro–Francia test, the uncategorized smooth test developed by Rayner & Best and Neyman's smooth goodness‐of‐fit test for composite hypotheses. 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 that 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 prior to the analysis. Results indicate that the MAXIMA data are compatible with Gaussianity.

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Section: Discussionmentioning

confidence: 99%

Goodness-of-fit tests to study the Gaussianity of the MAXIMA data

Cayón¹,

Argüeso²,

Martínez-González³

et al. 2003

Monthly Notices RAS

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“…With this statistic one can estimate the statistical significance of θ through the "Maximum Likelihood Method". Following the notation by Aliaga et al (2003), the score statistic for this goodness-of-fit test is…”

Section: Smooth Tests Of Goodness-of-fitmentioning

confidence: 99%

“…Aliaga et al 2003Aliaga et al , 2005. We used the five first statistics U 2 i which can be related to the k-order moments as follows,…”

Section: Smooth Tests Of Goodness-of-fitmentioning

confidence: 99%

“…Among those methods, we can mention the estimator for non-Gaussianity based on the CMB bispectrum (Ferreira et al 1998;Magueijo 2000), geometrical estimators on the sphere (Barreiro et al 2001;Monteserín et al 2005Monteserín et al , 2006 Minkowski functionals (Gott et al 1990;Komatsu et al 2003), goodness-of-fit tests (Rayner & Best 1989;Aliaga et al 2003;Barreiro et al 2007), wavelets (Ferreira et al 1997;Hobson et al 1999;Barreiro et al 2000) and steerable filters to search alignment structures (Wiaux et al 2006). Some of them have been applied to the CMB giving different results.…”

Section: Introductionmentioning

confidence: 99%

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Testing Gaussianity on Archeops data

Curto

Aumont

Macías-Pérez

et al. 2007

A&A

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Aims. We performed a Gaussianity analysis using a goodness-of-fit test and the Minkowski functionals on the sphere to study the measured Archeops Cosmic Microwave Background (CMB) temperature anisotropy data for a 143 GHz Archeops bolometer. We consider large angular scales, greater than 1.8 degrees, and a large fraction of the North Galactic hemisphere, around 16%, with a galactic latitude b > 15 degrees. Methods. The considered goodness-of-fit test, first proposed by Rayner & Best (1989, Smooth Tests of Goodness of Fit), was applied to the data after a signal-to-noise decomposition. The three Minkowski functionals on the sphere were used to construct a χ 2 statistic using different thresholds. The former method was calibrated using simulations of Archeops data containing the CMB signal and instrumental noise in order to check its asymptotic convergence. Two kind of maps produced with two different map-making techniques (coaddition and Mirage) are analysed. Results. Archeops maps for both Mirage and coaddition map-making, are compatible with Gaussianity. From these results we can exclude a dust and atmospheric contamination larger than 7.8% (90% CL). Also the non-linear coupling parameter f nl can be constrained to be f nl = 200 +1100 −800 at the 95% CL and on angular scales of 1.8 degrees. For comparison, the same method was applied to data from the NASA WMAP satellite in the same region of sky. The 1-year and 3-year releases were used. Results are compatible with those obtained with Archeops, implying in particular an upper limit for f nl on degree angular scales.

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“…Moreover if the data are Gaussian, they also follow a normal distribution and are independent. This decorrelation technique has been used for analysing the MAXIMA data with different smooth tests of gof [11,1,2]. Nevertheless, the preprocessing of the data has been improved in subsequent works through the use of a signal-to-noise decomposition, which is explained in the next subsection.…”

Section: The Rayner and Best Smooth Tests Of Goodness Of Fitmentioning

confidence: 99%

Gaussian Analysis of the CMB with the Smooth Tests of Goodness of Fit

Barreiro

Rubiño-Martín

Martínez-González

Highlights of Spanish Astrophysics IV

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The study of the Gaussianity of the cosmic microwave background (CMB) radiation is a key topic to understand the process of structure formation in the Universe. In this paper, we review a very useful tool to perform this type of analysis, the Rayner & Best smooth tests of goodness of fit. We describe how the method has been adapted for its application to imaging and interferometric observations of the CMB and comment on some recent and future applications of this technique to CMB data.

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Tests of Gaussianity

Cited by 6 publications

References 15 publications

Goodness-of-fit tests to study the Gaussianity of the MAXIMA data

Goodness-of-fit tests to study the Gaussianity of the MAXIMA data

Testing Gaussianity on Archeops data

Gaussian Analysis of the CMB with the Smooth Tests of Goodness of Fit

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