Inference about rare events: parallels in the asymptotics of unobserved probability and tail estimation

Abstract:

Consider the following two archetypal rare event problems: the estimation of the probability of (discrete) unobserved outcomes, and the estimation of the probability of (continuous) exceedance events, or tail estimation. In this talk we attempt to describe these problems from a common perspective, by analyzing them within the same theoretical framework of asymptotic statistics. In particular, we characterize discrete distributions with a rate parameter that closely relates to the heavy tail index in extreme value theory, and show that this parameter governs the mean asymptotic behavior of the probability of unobserved outcomes.

Biography:

Mesrob received his B.Eng. in Computer and Communications Engineering from the American University of Beirut in 2002, and his S.M. in Information Technology from MIT in 2005. He is currently at MIT, working towards a Ph.D. in Electrical Engineering and Computer Science. His research interest is in statistics and system theory, with applications to rare events, empirical processes, machine learning and information theory.