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Prediction regions for bivariate extreme events

Hall, P and Tajvidi, Nader LU (2004) In Australian & New Zealand Journal of Statistics 46(1). p.99-112
Abstract
This paper suggests using a mixture of parametric and non-parametric methods to construct prediction regions in bivariate extreme-value problems. The non-parametric part of the technique is used to estimate the dependence function, or copula, and the parametric part is employed to estimate the marginal distributions. A bootstrap calibration argument is suggested for reducing coverage error. This combined approach is compared with a more parametric one, relative to which it has the advantages of being more flexible and simpler to implement. It also enjoys these features relative to predictive likelihood methods. The paper shows how to construct both compact and semi-infinite bivariate prediction regions, and it treats the problem of... (More)
This paper suggests using a mixture of parametric and non-parametric methods to construct prediction regions in bivariate extreme-value problems. The non-parametric part of the technique is used to estimate the dependence function, or copula, and the parametric part is employed to estimate the marginal distributions. A bootstrap calibration argument is suggested for reducing coverage error. This combined approach is compared with a more parametric one, relative to which it has the advantages of being more flexible and simpler to implement. It also enjoys these features relative to predictive likelihood methods. The paper shows how to construct both compact and semi-infinite bivariate prediction regions, and it treats the problem of predicting the value of one component conditional on the other. The methods are illustrated by application to Australian annual maximum temperature data. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
likelihood, smoothing parameter, spline, predictive, non-parametric curve estimation, dependence function, cross-validation, copula, convex hull, bootstrap, calibration
in
Australian & New Zealand Journal of Statistics
volume
46
issue
1
pages
99 - 112
publisher
Wiley-Blackwell
external identifiers
  • wos:000220783400012
  • scopus:1842815877
ISSN
1467-842X
DOI
10.1111/j.1467-842X.2004.00316.x
language
English
LU publication?
yes
id
73d99ba9-870e-4cd8-a850-b1cb984e2b61 (old id 281712)
date added to LUP
2007-10-29 10:48:38
date last changed
2017-07-30 04:36:23
@article{73d99ba9-870e-4cd8-a850-b1cb984e2b61,
  abstract     = {This paper suggests using a mixture of parametric and non-parametric methods to construct prediction regions in bivariate extreme-value problems. The non-parametric part of the technique is used to estimate the dependence function, or copula, and the parametric part is employed to estimate the marginal distributions. A bootstrap calibration argument is suggested for reducing coverage error. This combined approach is compared with a more parametric one, relative to which it has the advantages of being more flexible and simpler to implement. It also enjoys these features relative to predictive likelihood methods. The paper shows how to construct both compact and semi-infinite bivariate prediction regions, and it treats the problem of predicting the value of one component conditional on the other. The methods are illustrated by application to Australian annual maximum temperature data.},
  author       = {Hall, P and Tajvidi, Nader},
  issn         = {1467-842X},
  keyword      = {likelihood,smoothing parameter,spline,predictive,non-parametric curve estimation,dependence function,cross-validation,copula,convex hull,bootstrap,calibration},
  language     = {eng},
  number       = {1},
  pages        = {99--112},
  publisher    = {Wiley-Blackwell},
  series       = {Australian & New Zealand Journal of Statistics},
  title        = {Prediction regions for bivariate extreme events},
  url          = {http://dx.doi.org/10.1111/j.1467-842X.2004.00316.x},
  volume       = {46},
  year         = {2004},
}