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.

中文翻译：

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比率统计的截断估计及其在重尾分布中的应用

从截断估计的角度重新讨论了重尾指数的估计问题。引入了一类新颖的估计器，该估计器基于固定大小的样本具有保证的准确性。这些估计器的性能在理论上和仿真中都通过大量相关示例进行了量化。还表明，在某些情况下，拟议的估计量在对数因子内达到了最优的参数收敛速度。建立了所提出估计量的一致渐近正态性的性质。