Bayesian Estimation of a Tail-Index with Marginalized Threshold

Douglas E. Johnston; Petar M. Djuric

ICASSP 2021accepted0 citations

Bayesian Estimation of a Tail-Index with Marginalized Threshold

Abstract

In this paper, we develop a new method for estimating the tail-index found in extreme value statistics. Using a fixed quantile, model-selection approach, we derive the posterior distribution of the tail-index marginalizing out the unknown threshold and nuisance parameters. Our marginalized threshold method relies on a spliced likelihood density for the bulk and extreme tail of the underlying distribution where the switch-point is specified as a fixed quantile. We derive a closed form expression for the posterior of the tail-index and illustrate its application to quantile, or value-at-risk, estimation. Our simulation results show that the marginalized threshold outperforms the maximum likelihood method, or the Hill estimate, for both tail-index and quantile estimation. We also illustrate our method using returns for the S&P 500 stock market index from 1928 - 2020.

BibTeX

@inproceedings{icassp2021_bayesianestimati,
  title = {Bayesian Estimation of a Tail-Index with Marginalized Threshold},
  author = {Douglas E. Johnston and Petar M. Djuric},
  booktitle = {ICASSP 2021},
  year = {2021}
}