Confidence regions for high quantiles of a heavy tailed distribution

Abstract

Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.

Reference

Liang Peng, Yongcheng Qi “Confidence regions for high quantiles of a heavy tailed distribution” (2006) DOI: 10.1214/009053606000000416

@Article{peng2006,
  title = {Confidence regions for high quantiles of a heavy tailed distribution},
  volume = {34},
  issn = {0090-5364, 2168-8966},
  url = {https://projecteuclid.org/euclid.aos/1162567639},
  doi = {10.1214/009053606000000416},
  abstract = {Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.},
  language = {en},
  number = {4},
  urldate = {2020-06-27},
  journal = {Annals of Statistics},
  author = {Peng, Liang and Qi, Yongcheng},
  month = {aug},
  year = {2006},
  mrnumber = {MR2283723},
  zmnumber = {1246.62125},
  note = {Publisher: Institute of Mathematical Statistics},
  keywords = {Confidence region, data tilting, empirical likelihood method, heavy tail, high quantile},
  pages = {1964--1986},
  custom-url-pdf = {https://projecteuclid.org/journalArticle/Download?urlId=10.1214%2F009053606000000416}
}