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Name: Holger Drees

Talk Title: Bootstrap for block-based extreme value statistics

Abstract: Let $(X_t)_{1\le t\le n}$ be a stationary $\mathbb{R}^d$-valued time series. In recent years, the asymptotic behavior of extreme value statistics of disjoint blocks $(X_{(i-1)l_n+j})_{1\le j\le l_n}$, $1\le i\le [n/l_n]$, or sliding blocks $(X_{i-1+j})_{1\le j\le l_n}$, $1\le i\le n-l_n+1$, has been thoroughly  studied. Usually, such limit theorems do not directly lend themselves to the construction of confidence intervals, because the influence of the underlying serial dependence structure on the limit distribution is too intricate. Taking up an approach by Drees and Neblung (2021), we present an abstract bootstrap result which applies both to statistics based on disjoint blocks and on sliding blocks. However, the multiplier bootstrap of sliding blocks requires to select an additional larger block length as a tuning parameter, which complicates the construction of confidence sets in practice. \bigskip {\bf References} \smallskip {\sc Drees, H.,} and {\sc Neblung, S.} (2021). Asymptotics for sliding blocks estimators of rare events. {\em Bernoulli} {\bf 27}, 1239--1269.

This talk is an invited talk at EVA 2021. View the programme here.