The block maximum method, which is widely used in extreme value analysis, uses a generalized extreme value distribution to approximate that of the maximum of m observations. The quality of this approximation depends on the value of m and may be poor if m is too small. Surprisingly little attention has been paid to the choice of the block length, although a good choice is crucial to the success of the method. In this paper we assess the effect of taking excessively long blocks in terms of asymptotic relative efficiency, and propose likelihood-based approaches and graphical diagnostics to determine whether a proposed block length is suitable, allowing for potential rounding and left-censoring of observations. We investigate our ideas using simulation and illustrate them using wind speed, river flow and rainfall data.

翻译：块最大值法在极值分析中广泛应用，该方法采用广义极值分布来近似拟合由m个观测值构成的最大值的分布。该近似的精确性取决于m的取值，当m过小时可能会导致近似效果不佳。令人惊讶的是，尽管块长选择对于方法成功至关重要，但相关研究对其关注甚少。本文从渐近相对效率角度评估了采用过长分块的影响，并提出基于似然的方法和图形诊断工具，用于判断给定分块长度是否合理，同时考虑了观测值可能存在的取整和左删失情况。我们通过模拟实验验证了上述方法，并利用风速、河流流量和降雨量数据进行了实证分析。