Spatial dependence and space–time trend in extreme events

The statistical theory of extremes is extended to independent multivariate observations that are non-stationary both over time and across space. non-stationarity space controlled via the scedasis (tail scale) in marginal distributions. Spatial dependence stems from extreme value theory. We establish asymptotic for weighted sequential tail empirical process quantile based on all observations, taken results yield two tests homoscedasticity tail, one time. Further, we show common index can be estimated a pseudo-maximum likelihood procedure pooling (non-stationary dependent) observations. Our leading example application rainfall Northern Germany.