Extreme value analysis for time series is often based on the block maxima method, in particular for environmental applications. In the classical univariate case, the latter is based on fitting an extreme-value distribution to the sample of (annual) block maxima. Mathematically, the target parameters of the extreme-value distribution also show up in limit results for other high order statistics, which suggests estimation based on blockwise large order statistics. It is shown that a naive approach based on maximizing an independence log-likelihood yields an estimator that is inconsistent in general. A consistent, bias-corrected estimator is proposed, and is analyzed theoretically and in finite-sample simulation studies. The new estimator is shown to be more efficient than traditional counterparts, for instance for estimating large return levels or return periods.

翻译：时间序列的极值分析通常基于分块最大值法，特别是在环境应用中。在经典的单变量情况下，该方法通过将极值分布拟合到（年度）分块最大值的样本来实现。从数学角度，极值分布的目标参数也出现在其他高阶统计量的极限结果中，这提示了基于分块大顺序统计量的估计方法。研究表明，基于最大化独立对数似然的朴素方法通常会产生不一致的估计量。本文提出了一种经过偏差校正的一致估计量，并从理论和有限样本模拟研究两方面进行了分析。新估计量在估计大重现水平或重现期等任务中，被证明比传统方法更高效。