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-spaced 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：本文研究多元分布与指定分布是否存在差异的问题，并检验两个多元分布是否相等。研究中提出了一种基于经典半空间深度信息准则的可视化工具包，该工具包生成二维图像（与数据维度无关），尤其适用于高维分布的比较。该可视化工具包的直观可解释性促使我们构建检验统计量来解决相应的假设检验问题。我们证明基于相同信息准则所提检验具有相合性，并推导了在邻接/局部备择假设下检验统计量的渐近分布，从而能够计算这些检验的渐近功效。此外，所提检验的相关计算负担较小。更关键的是，当数据来自重尾分布等多种分布时，该检验方法的性能优于文献中许多现有检验，表明所提方法具有稳健性。最后，通过两个基准真实数据集展示了所提可视化工具包和检验的实用性。