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.

中文翻译：

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椭圆对称分布的视觉测试

我们基于从比例尺图得出的检验统计量，提出了关于椭圆对称分布族拟合优度的视觉检验。比例尺比例图是根据中央等级区域的体积功能构建的。该测试是通过多元正态分布激发的，并扩展到椭圆对称性的测试。我们推导了检验统计量的渐近性质，并针对拟合优度检验和椭圆对称检验进行了详细的功效研究。我们还将拟议测试的性能与一些知名替代产品进行比较。