A Graphical Goodness-of-Fit Test for Dependence Models in Higher Dimensions

The test is based on pairs of variables and can thus be interpreted as a first-order approximation of the underlying dependence structure. The idea is to first transform pairs of data columns with the Rosenblatt transform to bivariate standard uniform distributions under the null hypothesis.

This hypothesis can be graphically tested with a matrix of bivariate scatterplots, Q-Q plots, or other transformations. Furthermore, additional information can be encoded as background color, such as measures of association or (approximate) p -values of tests of independence. The proposed goodness-of-fit test is designed as a basic graphical tool for detecting deviations from a postulated, possibly high-dimensional, dependence model.