Asymptotic Normality of Extreme Value Estimators on C[0,1]

CentER Discussion Paper No. 2003-132

25 Pages Posted: 24 Jun 2004

See all articles by John H. J. Einmahl

John H. J. Einmahl

Tilburg University - Department of Econometrics & Operations Research

Tao Lin

Erasmus University Rotterdam (EUR) - Eurandom Program

Date Written: 2003

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.

Keywords: Estimation, infinite dimensional systems, convergence, statistics

Suggested Citation

Einmahl, John H. J. and Lin, Tao, Asymptotic Normality of Extreme Value Estimators on C[0,1] (2003). CentER Discussion Paper No. 2003-132, Available at SSRN: https://ssrn.com/abstract=556979 or http://dx.doi.org/10.2139/ssrn.556979

John H. J. Einmahl (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O. Box 90153
5000 LE Tilburg
Netherlands

Tao Lin

Erasmus University Rotterdam (EUR) - Eurandom Program ( email )

Burgemeester Oudlaan 50
3000 DR Rotterdam, Zuid-Holland 3062PA
Netherlands

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