Hill, Bootstrap and Jackknife Estimators for Heavy Tails

Posted: 21 Jan 1997


We perform an analysis of tail index estimation through Monte-Carlo simulations of synthetic data, in order to evaluate several tail estimators proposed in the literature. We derive and discuss the error of the Hill estimator under a general tail expansion of the distribution function. The analysis is extended to study the behavior of tail estimation under aggregation. A detailed description is given of an algorithm designed to reduce the bias of the Hill estimator. This algorithm is based on a subsample bootstrap combined with the jackknife method. We show through simulations that this algorithm gives reasonable estimations of the tail index provided the number of observations is sufficiently large. The bias of the Hill estimator is successfully reduced. We also show that the estimation gives a constant tail index under aggregation up to an aggregation factor of 12. We recommend this method as a standard for tail estimation of empirical data.

JEL Classification: C15

Suggested Citation

Pictet, Olivier V. and Dacorogna, Michel M. and Müller, Ulrich A., Hill, Bootstrap and Jackknife Estimators for Heavy Tails. Available at SSRN: https://ssrn.com/abstract=4572

Olivier V. Pictet (Contact Author)

Pictet Asset Management ( email )


Michel M. Dacorogna

DEAR-Consulting ( email )

Scheuchzerstrasse 160
Zurich, 8057
+41795447327 (Phone)

Ulrich A. Müller

Olsen & Associates ( email )

Seefeldstrasse 233
CH-8008 Zurich
+41 (1) 386 48 16 (Phone)
+41 (1) 422 22 82 (Fax)

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