Confidence intervals for the tail index

Shihong Cheng; Liang Peng

doi:10.2307/3318540

Confidence intervals for the tail index

Shihong Cheng^*, Liang Peng

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

37 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	751-760
Number of pages	10
Journal	Bernoulli
Volume	7
Issue number	5
DOIs	https://doi.org/10.2307/3318540
Publication status	Published - 2001
Externally published	Yes

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title = "Confidence intervals for the tail index",

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 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.",

keywords = "Confidence interval, Coverage accuracy, Hill estimator, Tail index",

author = "Shihong Cheng and Liang Peng",

year = "2001",

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AU - Cheng, Shihong

AU - Peng, Liang

PY - 2001

Y1 - 2001

N2 - 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 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.

AB - 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 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.

KW - Confidence interval

KW - Coverage accuracy

KW - Hill estimator

KW - Tail index

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U2 - 10.2307/3318540

DO - 10.2307/3318540

M3 - Article

SN - 1350-7265

VL - 7

SP - 751

EP - 760

JO - Bernoulli

JF - Bernoulli

IS - 5

ER -

Confidence intervals for the tail index

Abstract

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