The Annals of Statistics

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

Laurens de Haan and Tao Lin

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 16 January 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1074290334

Digital Object Identifier
doi:10.1214/aos/1074290334

Mathematical Reviews number (MathSciNet)
MR2036397

Zentralblatt MATH identifier
1055.62059

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

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

Citation

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. https://projecteuclid.org/euclid.aos/1074290334


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