Advanced

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:
author
organization
publishing date
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
Inst 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
2007-08-23 09:18:28
date last changed
2017-02-08 13:49:29
@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},
  keyword      = {peaks over,threshold,generalized Pareto distribution,extreme value,exceedence,domain of attraction,coverage accuracy,bootstrap,calibration},
  language     = {eng},
  number       = {3},
  pages        = {875--895},
  publisher    = {Inst 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},
  volume       = {30},
  year         = {2002},
}