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Large deviations of tail estimators based on the Pareto approximation

Published online by Cambridge University Press:  14 July 2016

Richard L. Smith  and
Ishay Weissman
Richard L. Smith*
Affiliation:
University of Surrey
Ishay Weissman*
Affiliation:
Technion — Israel Institute of Technology
*
∗Postal address: Department of Mathematics, University of Surrey, Guildford GU2 5XH, UK.
∗∗Postal address: Faculty of Industrial Engineering and Management, Technion, Haifa, Israel.
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Abstract

We consider the relative error of a tail function when this is approximated by y–α using an estimator of Hill's for α. The results combine recent work of Davis and Resnick on tail estimation with Anderson's work on large deviations in extreme-value theory. Treating separately the domains of attraction of Φα and Λ, we obtain general conditions for the relative error to tend to 0 as u →∞, y → ∞ simultaneously. The results serve as warning against the automatic extrapolation of estimates based on extreme-value approximations.

Keywords

EXTREME VALUE THEORYREGULARLY VARYING FUNCTIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 619 - 630
Copyright
Copyright © Applied Probability Trust 1987 

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