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Drees, Holger; de Haan, Laurens; Resnick, Sidney

How to make a Hill plot. (English) Zbl 1106.62333

Ann. Stat. 28, No. 1, 254-274 (2000).
Summary: 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.

Cited in 69 Documents

MSC:

62G32 Statistics of extreme values; tail inference
62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions

Keywords:

Estimation; extreme value index; heavy tails; Hill estimator; order statistics; Pareto tails; regular variation
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Full Text: DOI Euclid

References:

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