Bernoulli

  • Bernoulli
  • Volume 7, Number 5 (2001), 751-760.

Confidence intervals for the tail index

Shihong Cheng and Liang Peng

Full-text: Open access

Abstract

One of the best-known estimators for the tail index of a heavy-tailed distribution is the Hill estimator. In this paper, confidence intervals based on the asymptotic normal approximation of the Hill estimator are studied. The coverage accuracy is evaluated and the theoretical optimal choice of the sample fraction for the one-sided confidence interval is given. One surprising finding is that the order of optimal coverage accuracy for the one-sided confidence interval depends on the sign of the second-order regular variation.

Article information

Source
Bernoulli, Volume 7, Number 5 (2001), 751-760.

Dates
First available in Project Euclid: 15 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1079399540

Mathematical Reviews number (MathSciNet)
MR2002g:62056

Zentralblatt MATH identifier
0985.62039

Keywords
confidence interval coverage accuracy Hill estimator tail index

Citation

Cheng, Shihong; Peng, Liang. Confidence intervals for the tail index. Bernoulli 7 (2001), no. 5, 751--760. https://projecteuclid.org/euclid.bj/1079399540


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