We introduce a kernel estimator, to the tail index of a right-censored Pareto-type distribution, that generalizes Worms's one (Worms and Worms, 2014)in terms of weight coefficients. Under some regularity conditions, the asymptotic normality of the proposed estimator is established. In the framework of the second-order condition, we derive an asymptotically bias-reduced version to the new estimator. Through a simulation study, we conclude that one of the main features of the proposed kernel estimator is its smoothness contrary to Worms's one, which behaves, rather erratically, as a function of the number of largest extreme values. As expected, the bias significantly decreases compared to that of the non-smoothed estimator with however a slight increase in the mean squared error.

翻译：我们引入一个内核估测器, 用于右审查的Pareto型分布的尾部指数, 以重量系数( Worms and Worms, 2014) 将虫子的分布( Worms and Worms, 2014) 概括为重量系数。 在某些正常条件下, 拟议的估测器的无症状常态性常态得以建立。 在第二阶条件的框架内, 我们从新的估测器获得一个无症状的偏差减少版本 。 通过模拟研究, 我们得出结论, 拟议的内核估测器的主要特征之一是它的平滑性与虫子的特征相反, 虫子的行为非常不稳定, 是最大极端值数的函数 。 正如预期的那样, 偏差与非经测算的估测器相比显著下降, 但平均平方误差略有增加 。