Mathematical theory suggests to model annual or seasonal maxima by the generalized extreme value distribution. In environmental applications like hydrology, record lengths are typically small, whence respective parameter estimators typically exhibit a large variance. The variance may be decreased by pooling observations from different sites or variables, but this requires to check the validity of the inherent homogeneity assumption. The present paper provides an overview of (partly new) respective asymptotic significance tests. It is found that the tests' levels are often violated in typical finite-sample situations, whence a parametric bootstrap approach based on max-stable process models is proposed to obtain more accurate critical values. As a side product, we present an overview of asymptotic results on a variety of common estimators for GEV parameters in a multisample situation of varying record lengths.

中文翻译：

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关于块极大值多元极值模型同质性统计检验的说明

数学理论建议通过广义极值分布来模拟年度或季节最大值。在水文等环境应用中，记录长度通常很小，因此各个参数估计器通常表现出很大的差异。通过汇集来自不同地点或变量的观察结果可以减少方差，但这需要检查固有同质性假设的有效性。本文概述了（部分新的）各自的渐近显着性检验。发现在典型的有限样本情况下经常违反测试水平，因此提出了基于最大稳定过程模型的参数引导方法以获得更准确的临界值。作为副产品，