Tail and Quantile Estimation for Real-Valued β-Mixing Spatial Data

This paper deals with extreme-value index estimation of a heavy-tailed distribution of a spatial dependent process. We are particularly interested in spatial rare events of a beta-mixing process. Given a stationary real-valued multidimensional spatial process {X-i, i is an element of Z(N)}, we investigate its heavy-tail index estimation. Asymptotic properties of the corresponding estimator are established under mild mixing conditions. The particularity of the tail proposed estimator is based on the spatial nature of the sample and its unbiased and reduced variance properties compared to well known tail index estimators. Extreme quantile estimation is also deduced. A numerical study on synthetic and real datasets is conducted to assess the finite-sample behaviour of the proposed estimators.