A moment estimator for the conditional extreme-value index

Abstract : 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.
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Submitted on : Tuesday, September 17, 2013 - 9:26:27 PM
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Gilles Stupfler. A moment estimator for the conditional extreme-value index. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2013, 7, pp.2298-2343. ⟨hal-00846594v3⟩

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