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Confidence intervals and accuracy estimation for heavy-tailed generalized Pareto distributions

Tajvidi, Nader LU (2004) In Extremes 6. p.111-123
Abstract
The generalized Pareto distribution (GPD) is a two-parameter family of distributions which can be used to model exceedances over a threshold. We compare the empirical coverage of some standard bootstrap and likelihood-based confidence intervals for the parameters and upper p-quantiles of the GPD. Simulation results indicate that none of the bootstrap methods give satisfactory intervals for small sample sizes. By applying a general method of D.N. Lawley, correction factors for likelihood ratio statistics of parameters and quantiles of the GPD have been calculated. Simulations show that for small sample sizes accuracy of confidence intervals can be improved by incorporating the computed correction factors to the likelihood-based confidence... (More)
The generalized Pareto distribution (GPD) is a two-parameter family of distributions which can be used to model exceedances over a threshold. We compare the empirical coverage of some standard bootstrap and likelihood-based confidence intervals for the parameters and upper p-quantiles of the GPD. Simulation results indicate that none of the bootstrap methods give satisfactory intervals for small sample sizes. By applying a general method of D.N. Lawley, correction factors for likelihood ratio statistics of parameters and quantiles of the GPD have been calculated. Simulations show that for small sample sizes accuracy of confidence intervals can be improved by incorporating the computed correction factors to the likelihood-based confidence intervals. While the modified likelihood method has better empirical coverage probability, the mean length of produced intervals are not longer than corresponding bootstrap confidence intervals. This article also investigates the performance of some bootstrap methods for estimation of accuracy measures of maximum likelihood estimators of parameters and quantiles of the GPD. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
confidence intervals, generalized Pareto distribution, maximum likelihood, small sample properties, Bartlett's correction, profile likelihood, bootstrap, quantiles
in
Extremes
volume
6
pages
111 - 123
publisher
Kluwer
ISSN
1572-915X
language
English
LU publication?
no
id
5fb129cc-6775-470d-bded-73ecfb4f3e74 (old id 698937)
date added to LUP
2007-12-05 15:30:53
date last changed
2016-06-29 09:02:43
@article{5fb129cc-6775-470d-bded-73ecfb4f3e74,
  abstract     = {The generalized Pareto distribution (GPD) is a two-parameter family of distributions which can be used to model exceedances over a threshold. We compare the empirical coverage of some standard bootstrap and likelihood-based confidence intervals for the parameters and upper p-quantiles of the GPD. Simulation results indicate that none of the bootstrap methods give satisfactory intervals for small sample sizes. By applying a general method of D.N. Lawley, correction factors for likelihood ratio statistics of parameters and quantiles of the GPD have been calculated. Simulations show that for small sample sizes accuracy of confidence intervals can be improved by incorporating the computed correction factors to the likelihood-based confidence intervals. While the modified likelihood method has better empirical coverage probability, the mean length of produced intervals are not longer than corresponding bootstrap confidence intervals. This article also investigates the performance of some bootstrap methods for estimation of accuracy measures of maximum likelihood estimators of parameters and quantiles of the GPD.},
  author       = {Tajvidi, Nader},
  issn         = {1572-915X},
  keyword      = {confidence intervals,generalized Pareto distribution,maximum likelihood,small sample properties,Bartlett's correction,profile likelihood,bootstrap,quantiles},
  language     = {eng},
  pages        = {111--123},
  publisher    = {Kluwer},
  series       = {Extremes},
  title        = {Confidence intervals and accuracy estimation for heavy-tailed generalized Pareto distributions},
  volume       = {6},
  year         = {2004},
}