Asymptotic Normality of Extreme Value Estimators on C[0,1]
CentER Discussion Paper No. 2003-132
25 Pages Posted: 24 Jun 2004
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: 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
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