A note on the CMH general association statistic and square contingency tables

In this expository note a simplified formula for the CMH general association statistic applicable to repeated categorical response data is given and applied to three-way square contingency tables

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

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.Comment: MNRAS, in pres

The goodness of fit publications of J.C.W. Rayner

This thesis has two parts. The first is an overview, The Development of the Smooth Tests of Goodness of Fit , of the submitted work. This overview is relatively brief, being approximately 5000 words long. The second part consists of the submitted publications themselves. These are listed below by year of publication, and alphabetically within year. The bulk of the thesis has necessitated it being bound in two volumes. The first volume consists of the overview and publications [1] to [18]. The second volume consists of publications [19] to [25]

Comparison of some tests of fit for the Laplace distribution

Tests for the Laplace distribution based on the sample skewness and kurtosis coefficients are shown to be related to components of smooth tests of goodness of fit and are compared with a number of tests including the Anderson-Darling test, a new data-driven smooth test, a new empirical characteristic function based test and a new maximum entropy test. This last would be our slight preference as the test of choice for testing for the Laplace distribution.

New smooth test statistics of goodness-of-fit for categorized composite null hypotheses

Composite parametric hypotheses, divergence-based statistics, generalized likelihood ratio statistics, generalized Wald statistics, multinomial distribution, smooth tests, goodness-of-fit, 62B10, 62E20,