2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information

2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information
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Paper Detail

Paper IDSPTM-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
SessionSPTM-23: Bayesian Signal Processing
LocationGather.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
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.