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

Abstract: This article inspects whether a multivariate distribution differs from a specified distribution and tests the equality of two low-dimensional 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 in- terpretability 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 en- ables 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 indi- cates 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 edited Camera Ready version, the following changes have been made:

1. First sentence of the abstract has been modified. The phrase "low-dimensional" has been added.
2. In the same spirit, the first sentence in the second paragraph in Section 1 has been modified.
3. The format of the algorithms has been changed. See pages 8 and 9.
4. The typo for the name "Martin Kružík." has been corrected.
5. Added Remark 5 and Theorem 2 (along with proof) at the end of the Section 3 on the discussion of the choice of M and d.

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

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

Assigned Action Editor: ~Jasper_C.H._Lee1

Submission Number: 6120