  In extreme value theory and other related risk analysis fields, probability
weighted moments (PWM) have been frequently used to estimate the parameters of
classical extreme value distributions. This method-of-moment technique can be
applied when second moments are finite, a reasonable assumption in many
environmental domains like climatological and hydrological studies. Three
advantages of PWM estimators can be put forward: their simple interpretations,
their rapid numerical implementation and their close connection to the
well-studied class of U-statistics. Concerning the later, this connection leads
to precise asymptotic properties, but non asymptotic bounds have been lacking
when off-the-shelf techniques (Chernoff method) cannot be applied, as
exponential moment assumptions become unrealistic in many extreme value
settings. In addition, large values analysis is not immune to the undesirable
effect of outliers, for example, defective readings in satellite measurements
or possible anomalies in climate model runs. Recently, the treatment of
outliers has sparked some interest in extreme value theory, but results about
finite sample bounds in a robust extreme value theory context are yet to be
found, in particular for PWMs or tail index estimators. In this work, we
propose a new class of robust PWM estimators, inspired by the median-of-means
framework of Devroye et al. (2016). This class of robust estimators is shown to
satisfy a sub-Gaussian inequality when the assumption of finite second moments
holds. Such non asymptotic bounds are also derived under the general
contamination model. Our main proposition confirms theoretically a trade-off
between efficiency and robustness. Our simulation study indicates that, while
classical estimators of PWMs can be highly sensitive to outliers.
