Nonparametric tail estimation using a double bootstrap method
Nonparametric tail estimation using a double bootstrap method
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DOI：
10.1016/s0167-9473(98)00060-7
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发表时间：
1998-12-28
影响因子：
1.8
通讯作者：
Van Dyck, J
中科院分区：
文献类型：
--
作者：
Caers, J;Van Dyck, J
极值理论导致了分布尾的非参数估计的各种统计方法的发展。在所有这些估计中，一个共同的问题是选择在估计中应该使用的极值数据的数量，以及在估计量上构造置信区间。在本文中，我们概述了一种使用非参数自举法来解决这两个问题的方法。bootstrap有两个方面：(1)第一个bootstrap用于估计最优极值数量——在均方误差意义上——用于尾指数估计，如Hall （1990， J. Multivariate Anal. 32(1990) 177-203）所建议的那样，(2)第二个bootstrap用于获得置信区间。该方法已应用于蒙特卡罗模拟产生的各种分布的数据，并在此基础上评估该方法的性能。(C) 1999 Elsevier Science B.V.版权所有
Extreme value theory has led to the development of various statistical methods for nonparametric estimation of distribution tails. A common problem in all of these estimators is the choice of the number of extreme data that should be used in the estimation and the construction of confidence intervals on the estimator. In this paper, we outline a method that uses the nonparametric bootstrap for both problems. The bootstrap is twofold: (1) the first bootstrap is used to estimate the optimal number of extremes - in the mean square error sense - to be used for the tail index estimation as has been earlier suggested by Hall (1990, J. Multivariate Anal. 32 (1990) 177-203), and (2) the second bootstrap is used to obtain confidence intervals. The method has been applied to data generated by Monte Carlo simulation for a variety of distributions and on this basis the performance of the method will be assessed. (C) 1999 Elsevier Science B.V. All rights reserved.