Inspecting discrepancy between multivariate distributions using half-space depth-based information criteria

TMLR Paper6120 Authors

Abstract:

This article inspects whether a multivariate distribution differs from a specified distribution and tests the equality of two multivariate distributions. In 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. 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. Moreover, the asymptotic distributions of the test statistics under contiguous/local alternatives are derived, which enables us to compute the asymptotic power of these tests. Empirical studies demonstrate that these tests outperform several existing methods across a range of distributions, which indicates that the proposed methodology is robust as well. The practical utility of the proposed toolkit and tests is further illustrated through applications to two benchmark real-world
datasets.

Submission Type: Long submission (more than 12 pages of main content)

Changes Since Last Submission: This submission was desk-rejected on October 2, 2025, at 17:19, due to the use of an incorrect template. We have now prepared the manuscript using the official TMLR template and are resubmitting the same article.

Assigned Action Editor: ~Jasper_C.H._Lee1

Submission Number: 6120