Probability and statistics seminar
Wednesday, 14th Feb, 4 pm--5pm
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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).