基于三阶条件下的降偏差重尾指数估计

在三阶条件下,提出了一种修正的降偏差估计,并讨论了其渐近性质及给出了相应的证明.在保证方差不变的前提下,不仅证明了在一定条件下该估计的渐近偏差更小,而且MonteCarlo模拟表明在有限样本情形下的模拟偏差也更小.

Reduced-bias heavy-tailed index estimation under a third order framework

Heavy-tailed index estimation has received much concern. In this paper,a modified reduced-bias estimator is proposed and its asymptotic properties are discussed,and the corresponding proof is given under a third order framework. Under the premise that the variance is constant,not only the asymptotic biases of the estimators proposed by us are smaller,but also the simulation biases are smaller for the finite samples through Monte-Carlo simulations.