Multiple block sizes and overlapping blocks for multivariate time series extremes
多元时间序列极值中的多重块长与重叠分块AI 解读 ↓
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多元时间序列极值中的多重块长与重叠分块
- 研究问题
- 在块长有限且不同块之间存在依赖的多元时间序列中，重叠分块与多种块长聚合能否改善块最大值估计的渐近表现？
- 方法与思路
- 作者比较重叠与不相交块最大值的经验分布及经验 copula，推导对块长统一的函数中心极限定理，并研究聚合与偏差校正。
- 材料陈述的贡献
- 摘要称重叠块可统一改善相关估计的渐近方差而不增加渐近偏差，并建立多块长聚合和改进极值估计收敛率的理论。
- 阅读关注点
- 应核对时间依赖条件、块长增长范围、光滑泛函要求，以及聚合权重、偏差校正和二阶参数估计的具体限制。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；方差与偏差结论属于渐近结果，未给出有限样本幅度，也未指定金融风险应用。
原文摘要
Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations from a genuine extreme value distribution. In practice, however, block sizes are finite and observations from different blocks are dependent. Theory respecting the latter complications is not well developed, and, in the multivariate case, has only recently been established for disjoint blocks of a single block size. We show that using overlapping blocks instead of disjoint blocks leads to a uniform improvement in the asymptotic variance of the multivariate empirical distribution function of rescaled block maxima and any smooth functionals thereof (such as the empirical copula), without any sacrifice in the asymptotic bias. We further derive functional central limit theorems for multivariate empirical distribution functions and empirical copulas that are uniform in the block size parameter, which seems to be the first result of this kind for estimators based on block maxima in general. The theory allows for various aggregation schemes over multiple block sizes, leading to substantial improvements over the single block length case and opens the door to further methodology developments. In particular, we consider bias correction procedures that can improve the convergence rates of extreme-value estimators and shed some new light on estimation of the second-order parameter when the main purpose is bias correction.