The Annals of Statistics

Asymptotic normality of extreme value estimators on C[0,1]

John H. J. Einmahl and Tao Lin

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Consider n i.i.d. random elements on C[0,1]. We show that, under an appropriate strengthening of the domain of attraction condition, natural estimators of the extreme-value index, which is now a continuous function, and the normalizing functions have a Gaussian process as limiting distribution. A key tool is the weak convergence of a weighted tail empirical process, which makes it possible to obtain the results uniformly on [0,1]. Detailed examples are also presented.

Article information

Ann. Statist., Volume 34, Number 1 (2006), 469-492.

First available in Project Euclid: 2 May 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G32: Statistics of extreme values; tail inference 62G30: Order statistics; empirical distribution functions 62G05: Estimation
Secondary: 60G70: Extreme value theory; extremal processes 60F17: Functional limit theorems; invariance principles

Estimation extreme value index infinite-dimensional extremes weak convergence on C[0,1]


Einmahl, John H. J.; Lin, Tao. Asymptotic normality of extreme value estimators on C [0,1]. Ann. Statist. 34 (2006), no. 1, 469--492. doi:10.1214/009053605000000831.

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