Weak convergence of the tail empirical process for dependent sequences |
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Authors: | Holger Rootzén |
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Institution: | Chalmers University of Technology, SE-419 62 Gothenburg, Sweden; Gothenburg University, SE-419 62 Gothenburg, Sweden |
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Abstract: | This paper proves weak convergence in D of the tail empirical process–the renormalized extreme tail of the empirical process–for a large class of stationary sequences. The conditions needed for convergence are (i) moment restrictions on the amount of clustering of extremes, (ii) restrictions on long range dependence (absolute regularity or strong mixing), and (iii) convergence of the covariance function. We further show how the limit process is changed if exceedances of a nonrandom level are replaced by exceedances of a high quantile of the observations. Weak convergence of the tail empirical process is one key to asymptotics for extreme value statistics and its wide range of applications, from geoscience to finance. |
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Keywords: | primary 60G70 secondary 60F17 62G32 |
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