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 tool-kit and tests is further illustrated through applications to two benchmark real-world datasets.

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

Changes Since Last Submission:

In view of the Action Editor's comment, in the Camera Ready version, the following changes have been made:

1. On page 1, the authors' names and other details have been added along with the OpenReview link.
2. On page 7, in the middle part of Remark 3, the more detailed explanation is added to respond to the reviewer’s comment on the rescaling factor.
3. On pages 7 and 8, in the algorithms, the values of $M$ and $B$ have been provided (kindly see Step 1.1, Step 1.5, Step 2.1 and Step 2.4) following the reviewer's comment. In addition, in the spirit of the Reviewer's comment, a small discussion has been added on the choices of $M$ and $B$ on page 9 after step 2.6 in the algorithm.
4. On page 20, a formal acknowledgement has been added.

Video: https://www.youtube.com/watch?v=KowU1Hv2xS0

Code: https://github.com/pratimguhaniyogi/DDD

Assigned Action Editor: ~Jasper_C.H._Lee1

Submission Number: 6120