We consider bias reduced estimators of the extreme value index (EVI) in case of Pareto-type distributions and under all max-domains of attraction. To this purpose we revisit the regression approach started in Feuerverger and Hall (Ann. Stat. 27, 760–781, 1999) and Beirlant et al. (Extremes 2, 177–200, 1999) in the case of a positive EVI, and in Beirlant et al. (2005) for real-valued EVI. We generalize these approaches using ridge regression exploiting the mathematical fact that the bias tends to 0 when the number of top data points used in the estimation is decreased. The penalty parameter is selected by minimizing the asymptotic mean squared error of the proposed estimator. The accuracy and utility of the ridge regression estimators are studied using simulations and are illustrated with case studies on reinsurance claim size data as well as daily wind speed data.

中文翻译：

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极值指数的Ridge回归估计量

在帕累托型分布的情况下以及在所有最大吸引域下，我们都考虑了极值指数（EVI）的偏倚估计量。为了这个目的，我们重新审视在Feuerverger和霍尔（安。统计。开始回归方法27，760-781，1999）和Beirlant等。（极端2，177–200，1999）在EVI为阳性的情况下，以及在Beirlant等人中。（2005）用于实值EVI。我们利用岭回归利用这些数学事实来概括这些方法，该数学事实是当估计中使用的顶部数据点的数量减少时，偏差趋于0。通过最小化提出的估计器的渐进均方误差来选择惩罚参数。使用模拟研究了岭回归估计量的准确性和实用性，并通过对再保险理赔规模数据以及每日风速数据的案例研究进行了说明。