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August 2019 On posterior consistency of tail index for Bayesian kernel mixture models
Cheng Li, Lizhen Lin, David B. Dunson
Bernoulli 25(3): 1999-2028 (August 2019). DOI: 10.3150/18-BEJ1043

Abstract

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.

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Cheng Li. Lizhen Lin. David B. Dunson. "On posterior consistency of tail index for Bayesian kernel mixture models." Bernoulli 25 (3) 1999 - 2028, August 2019. https://doi.org/10.3150/18-BEJ1043

Information

Received: 1 December 2016; Revised: 1 March 2018; Published: August 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07066247
MathSciNet: MR3961238
Digital Object Identifier: 10.3150/18-BEJ1043

Keywords: heavy tailed distribution , kernel mixture model , normalized random measures , posterior consistency , tail index

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 3 • August 2019
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