Visual tests for elliptically symmetric distributions

We propose a visual test of goodness of fit for families of elliptically symmetric distributions based on a test statistic derived from scale-scale plots. The scale-scale plots are constructed based on the volume functionals of the central rank regions. The test is motivated through the multivariate normal distributions and extended to a test of elliptical symmetry. We derive the asymptotic properties of the test statistic, and we perform detailed power studies for the test of goodness of fit, as well as the test for elliptical symmetry. We also compare the performance of the proposed test with some well-known alternatives.