Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool

Abdul-Fattah Abu-Awwad (1, 2) , Véronique Maume-Deschamps (1, 2) , Pierre Ribereau (1, 2)

1 ICJ - Institut Camille Jordan
2 PSPM - Probabilités, statistique, physique mathématique

One of the main concerns in extreme value theory is to quantify the dependence between joint tails. Using stochastic processes that lack flexibility in the joint tail may lead to severe under-or over-estimation of probabilities associated to simultaneous extreme events. Following recent advances in the literature, a flexible model called max-mixture model has been introduced for modeling situations where the extremal dependence structure may vary with the distance. In this paper we propose a nonparametric model-free selection criterion for the mixing coefficient Our criterion is derived from a madogram, a notion classically used in geostatistics to capture spatial structures. The procedure is based on a nonlinear least squares between the theoretical madogram and the empirical one. We perform a simulation study and apply our criterion to daily precipitation over the East of Australia.

Mots clés: Max-mixture model; Madogram; Extremal dependence; Non- linear least squares; Max-stable model

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Abdul-Fattah Abu-Awwad, Véronique Maume-Deschamps, Pierre Ribereau. Fitting spatial max-mixture processes with unknown extremal dependence class: an exploratory analysis tool. Test, 2020, 29, ⟨10.1007/s11749-019-00663-5⟩. ⟨hal-01671380⟩