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August 2008 Statistics of extremes by oracle estimation
Ion Grama, Vladimir Spokoiny
Ann. Statist. 36(4): 1619-1648 (August 2008). DOI: 10.1214/07-AOS535

Abstract

We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing procedure. Our main result is an oracle type inequality for the Kullback–Leibler loss.

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Ion Grama. Vladimir Spokoiny. "Statistics of extremes by oracle estimation." Ann. Statist. 36 (4) 1619 - 1648, August 2008. https://doi.org/10.1214/07-AOS535

Information

Published: August 2008
First available in Project Euclid: 16 July 2008

zbMATH: 1282.62131
MathSciNet: MR2435450
Digital Object Identifier: 10.1214/07-AOS535

Subjects:
Primary: 62G08 , 62G32
Secondary: 62G05

Keywords: Extreme values , high quantiles , Hill estimator , Nonparametric adaptive estimation , probabilities of rare events

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 4 • August 2008
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