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September, 1985 Kernel Estimates of the Tail Index of a Distribution
Sandor Csorgo, Paul Deheuvels, David Mason
Ann. Statist. 13(3): 1050-1077 (September, 1985). DOI: 10.1214/aos/1176349656

Abstract

We introduce a new estimate of the exponent of a distribution whose tail varies regularly at infinity. This estimate is expressed as the convolution of a kernel with the logarithm of the quantile function, and includes as particular cases the estimates introduced by Hill and by De Haan. Under very weak conditions, we prove asymptotic normality, consistency and discuss the optimal choices of the kernel and of the bandwidth parameter.

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Sandor Csorgo. Paul Deheuvels. David Mason. "Kernel Estimates of the Tail Index of a Distribution." Ann. Statist. 13 (3) 1050 - 1077, September, 1985. https://doi.org/10.1214/aos/1176349656

Information

Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0588.62051
MathSciNet: MR803758
Digital Object Identifier: 10.1214/aos/1176349656

Subjects:
Primary: 62G05
Secondary: 62G30

Rights: Copyright © 1985 Institute of Mathematical Statistics

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Vol.13 • No. 3 • September, 1985
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