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

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Author Info
Einmahl, J.H.J.
Lin, T. (Tilburg University, Center for Economic Research)

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Abstract

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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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 132.

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Date of creation: 2003
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Handle: RePEc:dgr:kubcen:2003132

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  1. De Haan, L. & Stadtmuller, U., 1992. "Generalized Regular Variation of Second Order," Papers 9268-a, Erasmus University of Rotterdam - Econometric Institute.
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  1. Jonathan Hill, 2006. "On Functional Central Limit Theorems for Dependent, Heterogeneous Tail Arrays with Applications to Tail Index and Tail Dependence Estimators," Working Papers 0607, Florida International University, Department of Economics. [Downloadable!]
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