| Paper ID | SPTM-23.2 |
| Paper Title |
BAYESIAN ESTIMATION OF A TAIL-INDEX WITH MARGINALIZED THRESHOLD |
| Authors |
Douglas Johnston, Farmingdale State College, United States; Petar M. Djurić, Stony Brook University, United States |
| Session | SPTM-23: Bayesian Signal Processing |
| Location | Gather.Town |
| Session Time: | Friday, 11 June, 14:00 - 14:45 |
| Presentation Time: | Friday, 11 June, 14:00 - 14:45 |
| Presentation |
Poster
|
| Topic |
Signal Processing Theory and Methods: [SSP] Statistical Signal Processing |
| IEEE Xplore Open Preview |
Click here to view in IEEE Xplore |
| Virtual Presentation |
Click here to watch in the Virtual Conference |
| 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. |
