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Activity Number: 34 - Foundations in Bayesian Statistics
Type: Contributed
Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #305104
Title: Posterior Consistency of Tail Index for Bayesian Kernel Mixture Models
Author(s): Cheng Li* and Lizhen Lin and David Dunson
Companies: National University of Singapore and University of Notre Dame and Duke University
Keywords: normalized random measures; kernel mixture model; heavy tailed distribution; posterior consistency; tail index

Asymptotic theory of tail index estimation has been studied extensively in the frequentist literature on extreme values, but rarely in the Bayesian context. We investigate whether popular Bayesian kernel mixture models are able to support heavy tailed distributions and consistently estimate the tail index. We show that posterior inconsistency in tail index is surprisingly common for both parametric and nonparametric mixture models. We then present a set of sufficient conditions under which posterior consistency in tail index can be achieved, and verify these conditions for Pareto mixture models under general mixing priors.

Authors who are presenting talks have a * after their name.

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