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.

Statistical methods are proposed to select homogeneous locations when analyzing spatial block maxima data, such as in extreme event attribution studies. The methods are based on classical hypothesis testing using Wald-type test statistics, with critical values obtained from suitable parametric bootstrap procedures and corrected for multiplicity. A large-scale Monte Carlo simulation study finds that the methods are able to accurately identify homogeneous locations, and that pooling the selected locations improves the accuracy of subsequent statistical analyses. The approach is illustrated with a case study on precipitation extremes in Western Europe. The methods are implemented in an R package that allows easy application in future extreme event attribution studies.

Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series, respective estimators may be improved by calculating block maxima in an overlapping way. A proof of concept is provided that the latter finding also holds in situations that involve certain piecewise stationarities. A weak convergence result for an empirical process of central interest is provided, and, as a case-in-point, further details are worked out explicitly for the probability weighted moment estimator. Irrespective of the serial dependence, the estimation variance is shown to be smaller for the new estimator, while the bias was found to be the same or vary comparably little in extensive simulation experiments. The results are illustrated by Monte Carlo simulation experiments and are applied to a common situation involving temperature extremes in a changing climate.

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