A note on statistical tests for homogeneities in multivariate extreme value models for block maxima

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.