论文标题
一种使用截短样品序列估算尾部指数的新方法
A new method for estimating the tail index using truncated sample sequence
论文作者
论文摘要
本文提出了一种新的截断估计方法，以估计具有无限平均值或方差的极为重型分布的尾部指数$α$。我们不仅提供两个截断的估计量$ \hatα$和$ \hatα^{\ prime} $，分别用于估计$α$（$ 0 <α\ leq 1 $）和$α$（$ 1 <α\ leq 2 $），但也证明了它们的非统计属性。在估计误差，类型误差和估计器的幂中比较了六个已知估计量的数值仿真结果表明，两个新的截断估计器的性能总体上相当不错。
This article proposes a new method of truncated estimation to estimate the tail index $α$ of the extremely heavy-tailed distribution with infinite mean or variance. We not only present two truncated estimators $\hatα$ and $\hatα^{\prime}$ for estimating $α$ ($0<α\leq 1$) and $α$ ($1<α\leq 2$) respectively, but also prove their asymptotic statistical properties. The numerical simulation results comparing the six known estimators in estimating error, the Type I Error and the power of estimator show that the performance of the two new truncated estimators is quite good on the whole.
