Subhra Sankar Dhar, IIT Kanpur


Probability and statistics seminar

Wednesday, 14th Feb, 4 pm--5pm


Venue: Room 113, Maths Dept

Host: Siuli Mukhopadhyay

Speaker: Subhra Sankar Dhar

Affiliation:   IIT Kanpur

Title: Inspecting discrepancy between multivariate distributions using half-space depth

 Abstract: In this talk, we inspect whether a multivariate distribution is different from a specified distribution or not AND two multivariate distributions are equal or not. In the course of this study, a graphical toolkit using well-known half-spaced depth 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 toolkit motivates us to formulate test statistics to carry out the corresponding testing of hypothesis problems. It is established that the proposed tests are consistent, and the asymptotic distributions of the test statistics under contiguous/local alternatives are derived, which enables 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 toolkit and tests is shown on two benchmark real data sets. This is a joint work with Pratim Guha Niyogi (Johns Hopkins University, USA). 

Room No. 113, Department of Mathematics
Wed, February 14, 2024
Start Time
4:00pm-5:00pm IST
1 hour
Created by
Sun, February 11, 2024 8:43pm IST