Title: A semiparametric model for generalized Pareto regressions based on a dimension reduction assumption
Authors: Julien Hambuckers - University of Goettingen (Germany) [presenting]
Cedric Heuchenne - University of Liege (Belgium)
Olivier Lopez - Université Pierre et Marie Curie Paris VI (France)
Abstract: A regression model is considered 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 $\gamma(x)$; 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 normality of the estimators that we define, and propose an iterative algorithm in order to perform their practical implementation. Our results are supported by some simulations. To illustrate the proposed approach, the method is applied to a new database of operational losses from the bank UniCredit.