Bootstrapping Extreme Value Estimators
本文为极值理论中的尾部分位数过程建立了自助法模拟渐近展开，用于构造极值指数估计量的置信区间，并证明了阈值法下自助法置信区间的一致性，而分块最大值法则不成立。
This article develops a bootstrap analogue of the well-known asymptotic expansion of the tail quantile process in extreme value theory. One application of this result is to construct confidence intervals for estimators of the extreme value index such as the Probability Weighted Moment (PWM) estimator. For the peaks-over-threshold method, we show the bootstrap consistency of the confidence intervals. By contrast, the asymptotic expansion of the quantile process of the bootstrapped block maxima does not lead to a similar consistency result for the PWM estimator using the block maxima method. For both methods, We show by simulations that the sample variance of bootstrapped estimates can be a good approximation for the asymptotic variance of the original estimator. Supplementary materials for this article are available online.