This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using well-known half-space depth based information criteria is proposed, which is a two-dimensional plot, regardless of the dimension of the data, and it is even useful in comparing high-dimensional distributions. The simple interpretability of the proposed graphical tool-kit motivates us to formulate test statistics to carry out the corresponding testing of hypothesis problems. It is established that the proposed tests based on the same information criteria are consistent, and moreover, the asymptotic distributions of the test statistics under contiguous/local alternatives are derived, which enable us to compute the asymptotic power of these tests. Furthermore, it is observed that the computations associated with the proposed tests are unburdensome. Besides, these tests perform better than many other tests available in the literature when data are generated from various distributions such as heavy tailed distributions, which indicates that the proposed methodology is robust as well. Finally, the usefulness of the proposed graphical tool-kit and tests is shown on two benchmark real data sets.

翻译：本文研究了如何检验一个多元分布是否与指定分布存在差异，并检验两个多元分布是否相等。在此研究过程中，我们提出了一种基于常用半空间深度信息准则的图形工具包，该工具包呈现为二维图形，不受数据维度限制，甚至可用于比较高维分布。该图形工具包直观的可解释性促使我们构建检验统计量，以执行相应的假设检验问题。研究证明，基于相同信息准则提出的检验具有一致性，并且推导了检验统计量在局部备择假设下的渐近分布，从而能够计算这些检验的渐近功效。此外，所提出检验的计算负担较轻。更重要的是，当数据来自重尾分布等多种分布时，这些检验的性能优于文献中许多其他检验方法，表明所提出的方法也具有稳健性。最后，通过两个基准真实数据集展示了所提出图形工具包与检验方法的实用性。