ON THE DISJOINT AND SLIDING BLOCK MAXIMA METHOD FOR PIECEWISE STATIONARY TIME SERIES

• 成果类型: Article
• 署名作者: Buecher, Axel; Zanger, Leandra
• 署名单位: Heinrich Heine University Dusseldorf
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2260
• 发表日期: 2023
• 页码: 573-598
• 关键词: likelihood estimators; parameters; extremes

摘要

Modeling univariate block maxima by the generalized extreme value dis-tribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying station-ary time series, respective estimators may be improved by calculating block maxima in an overlapping way. A proof of concept is provided that the lat-ter finding also holds in situations that involve certain piecewise stationari-ties. A weak convergence result for an empirical process of central interest is provided, and further details are examplarily worked out for the proba-bility weighted moment estimator. Irrespective of the serial dependence, the asymptotic estimation variance is shown to be smaller for the new estimator. In extensive simulation experiments, the finite-sample variance was typically found to be smaller as well, while the bias stays approximately the same. The results are illustrated by Monte Carlo simulation experiments and are applied to a common situation involving temperature extremes in a changing climate.