The Annals of Statistics

Weak consistency of extreme value estimators in C[0,1]

Laurens de Haan and Tao Lin

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We prove that when the distribution of a stochastic process in C[0,1]$ is in the domain of attraction of a max-stable process, then natural estimators for the extreme-value index (which is now a continuous function) and for the mean measure of the limiting Poisson process are consistent in the appropriate topologies. The ultimate goal, estimating probabilities of small (failure) sets, will be considered later.

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Ann. Statist., Volume 31, Number 6 (2003), 1996-2012.

First available in Project Euclid: 16 January 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G32: Statistics of extreme values; tail inference 62H11: Directional data; spatial statistics

Extreme values convergence in $C[0,1]$


Haan, Laurens de; Lin, Tao. Weak consistency of extreme value estimators in C [0,1]. Ann. Statist. 31 (2003), no. 6, 1996--2012. doi:10.1214/aos/1074290334.

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