The Annals of Statistics

How to make a Hill plot

Holger Drees, Sidney Resnick, and Laurens de Haan

Full-text: Open access

Abstract

An abundance of high quality data sets requiring heavy tailed models necessitates reliable methods of estimating the shape parameter governing the degree of tail heaviness. The Hill estimator is a popular method for doing this but its practical use is encumbered by several difficulties. We show that an alternative method of plotting Hill estimator values is more revealing than the standard method unless the underlying data comes from a Pareto distribution.

Article information

Source
Ann. Statist., Volume 28, Number 1 (2000), 254-274.

Dates
First available in Project Euclid: 14 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1016120372

Digital Object Identifier
doi:10.1214/aos/1016120372

Mathematical Reviews number (MathSciNet)
MR1762911

Zentralblatt MATH identifier
1106.62333

Subjects
Primary: 60G75
Secondary: 62G05: Estimation 62G20: Asymptotic properties

Keywords
Estimation extreme value index heavy tails Hill estimator order statistics Pareto tails regular variation

Citation

Drees, Holger; de Haan, Laurens; Resnick, Sidney. How to make a Hill plot. Ann. Statist. 28 (2000), no. 1, 254--274. doi:10.1214/aos/1016120372. https://projecteuclid.org/euclid.aos/1016120372


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