论文标题
使用正则化估算帕累托型分布的尾部索引
Estimation of the tail index of Pareto-type distributions using regularisation
论文作者
论文摘要
在本文中，我们引入了降低偏置估计器的估计，以估计帕累托型分布的尾部指数。这是通过使用正规加权最小二乘和指数回归模型来实现的，用于最高阶统计的对数间隔。对所提出的估计量的渐近性质进行了分析研究，发现渐近公正，一致且正态分布。同样，通过模拟理论研究了估计量的有限样本行为。发现拟议的估计量产生较低的偏置和MSE。此外，通过估计保险行业索赔的基本分配的尾部指数来说明拟议的估计器。
In this paper, we introduce reduced-bias estimators for the estimation of the tail index of a Pareto-type distribution. This is achieved through the use of a regularised weighted least squares with an exponential regression model for log-spacings of top order statistics. The asymptotic properties of the proposed estimators are investigated analytically and found to be asymptotically unbiased, consistent and normally distributed. Also, the finite sample behaviour of the estimators are studied through a simulations theory. The proposed estimators were found to yield low bias and MSE. In addition, the proposed estimators are illustrated through the estimation of the tail index of the underlying distribution of claims from the insurance industry.
