Electronic Journal of Statistics

A moment estimator for the conditional extreme-value index

Gilles Stupfler

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In extreme value theory, the so-called extreme-value index is a parameter that controls the behavior of a distribution function in its right tail. Knowing this parameter is thus essential to solve many problems related to extreme events. In this paper, the estimation of the extreme-value index is considered in the presence of a random covariate, whether the conditional distribution of the variable of interest belongs to the Fréchet, Weibull or Gumbel max-domain of attraction. The pointwise weak consistency and asymptotic normality of the proposed estimator are established. We examine the finite sample performance of our estimator in a simulation study and we illustrate its behavior on a real set of fire insurance data.

Article information

Electron. J. Statist., Volume 7 (2013), 2298-2343.

First available in Project Euclid: 19 September 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties 62G30: Order statistics; empirical distribution functions 62G32: Statistics of extreme values; tail inference

Extreme-value index moment estimator random covariate consistency asymptotic normality


Stupfler, Gilles. A moment estimator for the conditional extreme-value index. Electron. J. Statist. 7 (2013), 2298--2343. doi:10.1214/13-EJS846. https://projecteuclid.org/euclid.ejs/1379596772

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