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December, 1984 Tail Estimates Motivated by Extreme Value Theory
Richard Davis, Sidney Resnick
Ann. Statist. 12(4): 1467-1487 (December, 1984). DOI: 10.1214/aos/1176346804


An estimate of the upper tail of a distribution function which is based on the upper $m$ order statistics from a sample of size $n(m \rightarrow \infty, m/n \rightarrow 0$ as $n \rightarrow \infty)$ is shown to be consistent for a wide class of distribution functions. The empirical mean residual life of the $\log$ transformed data and the sample $1 - m/n$ quantile play a key role in the estimate. The joint asymptotic behavior of the empirical mean residual life and sample $1 - m/n$ quantile is determined and rates of convergence of the estimate to the tail are derived.


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Richard Davis. Sidney Resnick. "Tail Estimates Motivated by Extreme Value Theory." Ann. Statist. 12 (4) 1467 - 1487, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0555.62035
MathSciNet: MR760700
Digital Object Identifier: 10.1214/aos/1176346804

Primary: 62G05
Secondary: 62F12 , 62G30

Keywords: Intermediate order statistics , mean residual life , Pareto distributions , regular variation , Tail estimation

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 4 • December, 1984
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