TY - GEN
T1 - Bayesian estimation of a tail-index with marginalized threshold
AU - Johnston, Douglas E.
AU - Djurić, Petar M.
N1 - Publisher Copyright: © 2021 IEEE
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Excess over threshold
KW - Extreme value theory
KW - Risk-management
KW - Value-at-risk
UR - https://www.scopus.com/pages/publications/85115175347
U2 - 10.1109/ICASSP39728.2021.9413935
DO - 10.1109/ICASSP39728.2021.9413935
M3 - Conference contribution
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 5569
EP - 5573
BT - 2021 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2021
Y2 - 6 June 2021 through 11 June 2021
ER -