Asymptotic properties of generalized DPR statistic |
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Authors: | Marijus Vai?iulis |
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Institution: | 1. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, LT-08663, Vilnius, Lithuania 2. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania
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Abstract: | We investigate asymptotic properties of the so-called generalized Davydov, Paulauskas, and Račkauskas statistic that was introduced
in V. Paulauskas and M. Vaičiulis, Several modifications of DPR estimator of the tail index, Lith. Math. J., 51(1):36–50, 2011]. We obtain an asymptotics of the bias of this statistic and show that this statistic is asymptotically
normal. As an application, we provide a new class of semiparametric heavy-tailed estimators and compare these estimators with
other estimators, including the popular Hill and Pickands estimators. |
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Keywords: | |
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