Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution
Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution
复制标题
单参数帕累托分布尾部指数的鲁棒高效估计
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
R. Serfling
中科院分区：
文献类型：
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作者：
V. Brazauskas;R. Serfling
摘要 单参数Pareto模型尾部指标参数的估计在精算等科学领域有着广泛的应用。在这里，我们从两个竞争标准的角度来检查各种估计量：效率和针对较高异常值的鲁棒性。由于最大似然估计器（MLE）高效但不鲁棒，我们希望替代估计器能够保留相对较高的效率，同时也足够鲁棒。引入了一种新的广义中值型估计器，并将其与 MLE 和几个与矩、修剪、最小二乘、分位数和百分位数匹配方法相关的成熟估计器进行了比较。人们发现矩量法和最小二乘估计量在这两个标准方面都相对有缺陷，应该变得不受欢迎，而截尾均值和广义中值估计量往往在其他竞争者中占主导地位。广义中位数类型总体表现最好。这些发现为修正和更新流行观点提供了基础。讨论的其他主题包括对上分位数、尾部概率和精算量的稳健估计的应用，例如与投资组合偿付能力相关的止损和超额损失再保险保费。将鲁棒参数方法与经验非参数方法进行比较，后者通常是非鲁棒的。
Abstract Estimation of the tail index parameter of a single-parameter Pareto model has wide application in actuarial and other sciences. Here we examine various estimators from the standpoint of two competing criteria: efficiency and robustness against upper outliers. With the maximum likelihood estimator (MLE) being efficient but nonrobust, we desire alternative estimators that retain a relatively high degree of efficiency while also being adequately robust. A new generalized median type estimator is introduced and compared with the MLE and several well-established estimators associated with the methods of moments, trimming, least squares, quantiles, and percentile matching. The method of moments and least squares estimators are found to be relatively deficient with respect to both criteria and should become disfavored, while the trimmed mean and generalized median estimators tend to dominate the other competitors. The generalized median type performs best overall. These findings provide a basis for revision and updating of prevailing viewpoints. Other topics discussed are applications to robust estimation of upper quantiles, tail probabilities, and actuarial quantities, such as stop-loss and excess-of-loss reinsurance premiums that arise concerning solvency of portfolios. Robust parametric methods are compared with empirical nonparametric methods, which are typically nonrobust.