Conditional tail and quantile estimation for real-valued β-mixing spatial data
Résumé
This paper deals with the estimation of the tail index of a conditionnal heavy-tailed distribution of a spatial process. We are particularly interested in the estimation of conditionnal spatial rare events when the process is β−mixing. Given a conditionnal stationary real-valued multidimensional spatial process Y x i , i ∈ Z N , we investigate its conditional heavy-tail index estimation and the corresponding conditional quantile. Asymptotic properties of the corresponding estimators 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 conditional tail index estimators. A numerical study on synthetic and real datasets is conducted to assess the finite-sample behaviour of the proposed estimators.
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