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.

翻译：块极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，基于非重叠块极大值的经典方法可以通过采用滑动块极大值得到普遍改进。然而，基于滑动块极大值的估计量的渐近方差公式涉及对某类多元极值分布协方差的积分，这使得其估计及一般性推断成为复杂问题。作为替代方案，可采用自助近似方法：我们证明即使在独立同分布情形下，时间序列分析中朴素的块自助方法也不具有一致性，并提出基于循环块极大值重采样的一致性替代方案。作为推论，我们证明了经典非重叠块极大值重采样自助法的一致性，并表明基于循环块极大值的估计量具有与滑动块极大值估计量相同的渐近方差。通过蒙特卡洛实验说明了有限样本性质，并通过降水极值的案例研究展示了这些方法。