A goodness-of-fit test for elliptical distributions with diagnostic capabilities

This paper develops a test of goodness-of-fit for elliptical distributions. The test is invariant to affine-linear transformations and has a convenient expression that can be broken into components containing diagnostic information to be used to identify possible departures when the test rejects. The test is developed for the bivariate Laplace, logistic and Pearson type II distributions, as well as the multivariate normal for which the R package ECGofTestDx is available on the CRAN. A simulation shows the usefulness of the diagnostic tools.