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Almost sure convergence of the Hill estimator

Published online by Cambridge University Press:  24 October 2008

Paul Deheuvels ,
Erich Haeusler  and
David M. Mason
Paul Deheuvels
Affiliation:
Université Paris VI, Paris, France
Erich Haeusler
Affiliation:
University of Delaware, Newark, Delaware, U.S.A.
David M. Mason
Affiliation:
Universität M¨nchen, Munich, Germany
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Abstract

In this note we characterize those sequences kn such that the Hill estimator of the tail index based on the kn upper order statistics of a sample of size n from a Pareto-type distribution is strongly consistent.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 371 - 381
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

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