基于块最大值法的引导估计器

Axel Bücher, Torben Staud
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引用次数: 0

摘要

块最大值法是分析潜在多元时间序列极值行为的标准方法。最近研究发现,通过考虑滑动块最大值,可以普遍改进基于不连续块最大值的经典方法。然而,基于滑动块最大值的估计值的渐近方差公式涉及到某一多元极值分布族的协方差的整数,这使得其估计和一般推断成为一个错综复杂的问题。作为一种替代方法,我们可以依靠自举近似:我们证明了时间序列分析中的天真块自举方法即使在 i.i.d.\ 情况下也是不一致的,并提供了一种基于循环块最大值重采样的一致替代方法。作为副产品,我们证明了经典的重采样引导法对不相邻的块最大值的一致性,并证明了基于循环块最大值的估计方法与其对应的滑动块最大值具有相同的渐近方差。蒙特卡罗实验说明了有限样本的特性,降水极值的案例研究也证明了这些方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Bootstrapping Estimators based on the Block Maxima Method
The block maxima method is a standard approach for analyzing the extremal behavior of a potentially multivariate time series. It has recently been found that the classical approach based on disjoint block maxima may be universally improved by considering sliding block maxima instead. However, the asymptotic variance formula for estimators based on sliding block maxima involves an integral over the covariance of a certain family of multivariate extreme value distributions, which makes its estimation, and inference in general, an intricate problem. As an alternative, one may rely on bootstrap approximations: we show that naive block-bootstrap approaches from time series analysis are inconsistent even in i.i.d.\ situations, and provide a consistent alternative based on resampling circular block maxima. As a by-product, we show consistency of the classical resampling bootstrap for disjoint block maxima, and that estimators based on circular block maxima have the same asymptotic variance as their sliding block maxima counterparts. The finite sample properties are illustrated by Monte Carlo experiments, and the methods are demonstrated by a case study of precipitation extremes.
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