A semiparametric model for Generalized Pareto regression based on a dimension reduction assumption

Julien Hambuckers (1) , Cédric Heuchenne , Olivier Lopez (2)

1 Georg-August-University = Georg-August-Universität Göttingen
2 LSTA - Laboratoire de Statistique Théorique et Appliquée

We consider a regression model in which the tail of the conditional distribution of the response can be approximated by a Generalized Pareto distribution. Our model is based on a semiparametric single-index assumption on the conditional tail index, while no further assumption on the conditional scale parameter is made. The underlying dimension reduction assumption allows the procedure to be of prime interest in the case where the dimension of the covariates is high, in which case the purely nonparametric techniques fail while the purely parametric ones are too rough to correctly fit to the data. We derive asymptotic properties of the resulting parameter estimators, and propose an iterative algorithm for their practical implementation. We study the finite sample behavior of our methodology through simulations. To exhibit the interest of the proposed approach in practice, the method is applied to a new database of operational losses from the bank UniCredit.

Mots clés: Curse-of-dimensionality; Extreme events; Semiparametric regression; Oper-ational loss

Domaines: Statistiques [math.ST]

Julien Hambuckers, Cédric Heuchenne, Olivier Lopez. A semiparametric model for Generalized Pareto regression based on a dimension reduction assumption. 2016. ⟨hal-01362314⟩