Effect of extrapolation on coverage accuracy of prediction intervals computed from Pareto-type data
Hall, P ; Peng, L and Tajvidi, Nader LU
(2002)
In Annals of Statistics
30(3).
p.875-895
- Abstract
- A feature that distinguishes extreme-value contexts from more conventional statistical problems is that in the former we often wish to make predictions well beyond the range of the data. For example, one might have a 10-year sequence of observations of a phenomenon, and wish to make forecasts for the next 20 to 30 years. It is generally unclear how such long ranges of extrapolation affect prediction. In the present paper, and for extremes from a distribution with regularly varying tails at infinity, we address this problem. We approach it in two ways: first, from the viewpoint of predictive inference under a model that is admittedly only approximate, and where the errors of greatest concern are caused by the interaction of long-range... (More)
- A feature that distinguishes extreme-value contexts from more conventional statistical problems is that in the former we often wish to make predictions well beyond the range of the data. For example, one might have a 10-year sequence of observations of a phenomenon, and wish to make forecasts for the next 20 to 30 years. It is generally unclear how such long ranges of extrapolation affect prediction. In the present paper, and for extremes from a distribution with regularly varying tails at infinity, we address this problem. We approach it in two ways: first, from the viewpoint of predictive inference under a model that is admittedly only approximate, and where the errors of greatest concern are caused by the interaction of long-range extrapolation with model misspecification; second, where the model is accurate but errors arise from a combination of extrapolation and the fact that the method is only approximate. In both settings we show that, in a way which can be defined theoretically and confirmed numerically, one can make predictions exponentially far into the future without committing serious errors. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/331822
- author
- Hall, P
; Peng, L
and Tajvidi, Nader
LU
- organization
- publishing date
- 2002
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- peaks over, threshold, generalized Pareto distribution, extreme value, exceedence, domain of attraction, coverage accuracy, bootstrap, calibration
- in
- Annals of Statistics
- volume
- 30
- issue
- 3
- pages
- 875 - 895
- publisher
- Institute of Mathematical Statistics
- external identifiers
-
- wos:000177354600010
- scopus:0036046063
- ISSN
- 0090-5364
- DOI
- 10.1214/aos/1028674844
- language
- English
- LU publication?
- yes
- id
- f86bf1a9-adcd-469c-92c3-85945170a290 (old id 331822)
- date added to LUP
- 2016-04-01 16:57:07
- date last changed
- 2022-01-28 23:17:30
@article{f86bf1a9-adcd-469c-92c3-85945170a290,
abstract = {{A feature that distinguishes extreme-value contexts from more conventional statistical problems is that in the former we often wish to make predictions well beyond the range of the data. For example, one might have a 10-year sequence of observations of a phenomenon, and wish to make forecasts for the next 20 to 30 years. It is generally unclear how such long ranges of extrapolation affect prediction. In the present paper, and for extremes from a distribution with regularly varying tails at infinity, we address this problem. We approach it in two ways: first, from the viewpoint of predictive inference under a model that is admittedly only approximate, and where the errors of greatest concern are caused by the interaction of long-range extrapolation with model misspecification; second, where the model is accurate but errors arise from a combination of extrapolation and the fact that the method is only approximate. In both settings we show that, in a way which can be defined theoretically and confirmed numerically, one can make predictions exponentially far into the future without committing serious errors.}},
author = {{Hall, P and Peng, L and Tajvidi, Nader}},
issn = {{0090-5364}},
keywords = {{peaks over; threshold; generalized Pareto distribution; extreme value; exceedence; domain of attraction; coverage accuracy; bootstrap; calibration}},
language = {{eng}},
number = {{3}},
pages = {{875--895}},
publisher = {{Institute of Mathematical Statistics}},
series = {{Annals of Statistics}},
title = {{Effect of extrapolation on coverage accuracy of prediction intervals computed from Pareto-type data}},
url = {{http://dx.doi.org/10.1214/aos/1028674844}},
doi = {{10.1214/aos/1028674844}},
volume = {{30}},
year = {{2002}},
}