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Characterising distributions and their tails using multivariate quantiles and depths.

PhD Thesis Defense
PhD Thesis Defense
When May 30, 2024
from 01:30 PM to 02:30 PM
Where LH-006, Ground Floor (Hybrid)
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Speaker: Sibsankar Singha (TIFR CAM)

Abstract:  In this talk, we focus on three prominent geometric measures: geometric quantiles, half-space depth, and optimal transport (OT) based quantiles (Monge quantiles). Our core objective is to establish connections between these geometric measures and their underlying distributions, addressing whether they capture essential aspects of probability measures, such as tail behaviors.
Numerous results are already available for the population-based analysis of these geometric measures, particularly in terms of their asymptotic (extreme) behaviour. Considering practical applications, the questions regarding asymptotics become even more critical when examining sample versions of these geometric measures. We establish convergence rates for the sample versions of quantiles and investigate the extreme behaviour of the geometric measures based on the type of the underlying distribution.

Additionally, we introduce few tools, such as multivariate Q-Q plots, to compare multivariate samples using optimal transport and entropy-regularized optimal transport. We also develop related statistical tests, enhancing the practical applicability of our findings.

Overall, this talk provides insights into the robustness and utility of the above mentioned geometric measures in understanding and comparing distributions through advanced statistical methods.

Zoom details are as follows:

Topic: PhD Thesis Defense by Sibsankar Singha
Time: May 30, 2024 01:30 PM Mumbai, Kolkata, New Delhi

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Meeting ID: 943 2109 8512
Passcode: 053660

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