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February 2006 Asymptotic normality of extreme value estimators on C[0,1]
John H. J. Einmahl, Tao Lin
Ann. Statist. 34(1): 469-492 (February 2006). DOI: 10.1214/009053605000000831


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.


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John H. J. Einmahl. Tao Lin. "Asymptotic normality of extreme value estimators on C[0,1]." Ann. Statist. 34 (1) 469 - 492, February 2006.


Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62041
MathSciNet: MR2275250
Digital Object Identifier: 10.1214/009053605000000831

Primary: 62G05 , 62G30 , 62G32
Secondary: 60F17 , 60G70

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

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2006
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