Tail index estimation for stationary spatial data

Hill estimator for the tail index of regularly varying data is extensively studied in the statistics literature. Its consistency has been established in various settings, including that of dependent sequences of random variables. Building on their results, we show that the Hill estimator is consistent also when applied to stationary spatial lattice models under suitable conditions. We further show how these conditions can be checked in the case of spatial moving averages and moving maxima with regularly varying noise. Based on joint work with Bojan Basrak.