Truncated estimation of ratio statistics with application to heavy tail distributions D. N. Politis, V. A. Vasiliev, S. E. Vorobeychikov
Material type:
ArticleSubject(s): распределения с тяжелыми хвостами | Парето распределение | оптимальная скорость сходимостиGenre/Form: статьи в журналах Online resources: Click here to access online
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Mathematical methods of statistics Vol. 27, № 3. P. 226-243Abstract: The problem of estimation of the heavy tail index is revisited from the point of view of truncated estimation. A class of novel estimators is introduced having guaranteed accuracy based on a sample of fixed size. The performance of these estimators is quantified both theoretically and in simulations over a host of relevant examples. It is also shown that in several cases the proposed estimators attain — within a logarithmic factor — the optimal parametric rate of convergence. The property of uniform asymptotic normality of the proposed estimators is established.
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The problem of estimation of the heavy tail index is revisited from the point of view of truncated estimation. A class of novel estimators is introduced having guaranteed accuracy based on a sample of fixed size. The performance of these estimators is quantified both theoretically and in simulations over a host of relevant examples. It is also shown that in several cases the proposed estimators attain — within a logarithmic factor — the optimal parametric rate of convergence. The property of uniform asymptotic normality of the proposed estimators is established.
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