重尾分布二阶参数的半参数估计

Semi-parameter estimation of second order parameter for heavy-tailed distribution

重尾分布二阶参数在极值理论中扮演着重要的角色,尤其是重尾指数估计中门限的最优选取,以及重尾指数降偏差估计的渐近偏差都取决于二阶参数p.基于统计量M_(n^(a))(k),提出了重尾分布二阶参数的半参数估计,在极值理论的二阶正则条件下,得到二阶参数半参数估计的相合性,在三阶正则条件下得到其渐近正态性.通过Monte-Carlo模拟,从大样本性质与小样本性质这两方面,对提出的半参数估计进行比较.结果表明,本文的估计,在大样本性质方面,表现较优;在小样本性质方面,一定范围内表现得更好.

The second order parameter of heavy-tailed is of primordial importance m extreme value theory. Especially, the adaptive choice of the best threshold to be considered in the estimation of the heavy tailed index and the classical estimators of heavy-tailed index trying to reduce the main component of their asymptotic bias, which depend strongly on p. Based on the statistics Mn^（α）（k）, we present the semi-parameter estimation of the second order pararneter of heavy-tailed distribution. We prove the consistency of the second order parameter under the second order condition in extreme value theory, and prove asymptotic normality under the third order condition. We compare the estimators provided in two aspects of large sample behavior and small sample behavior through Monte-Carlo techniques. The conclusion is that the performance of the new estimator is better in large sample behavior and is better in the certain range in small sample behavior.