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October 2001 Confidence intervals for the tail index
Shihong Cheng, Liang Peng
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Bernoulli 7(5): 751-760 (October 2001).


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.


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Shihong Cheng. Liang Peng. "Confidence intervals for the tail index." Bernoulli 7 (5) 751 - 760, October 2001.


Published: October 2001
First available in Project Euclid: 15 March 2004

zbMATH: 0985.62039
MathSciNet: MR2002G:62056

Keywords: Confidence interval , coverage accuracy , Hill estimator , tail index

Rights: Copyright © 2001 Bernoulli Society for Mathematical Statistics and Probability

Vol.7 • No. 5 • October 2001
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