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

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 and 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.