Bias Reduced Peaks over Threshold Tail Estimation

Abstract

Bias reduction in tail estimation has mainly been performed in case of Pareto-type models; see for instance Drees (1996), Peng (1998), Feuerverger and Hall (1999), Beirlant et al. (1999, 2002), Gomes and Martins (2002) and Caeiro et al. (2005, 2009). In that context, Beirlant et al. (2009) and Papastathopoulos and Tawn (2013) constructed distributional models that are based on second order rates of convergence for distributions of peaks over thresholds (POT). Such approach also allows to connect the tail and the bulk of the distribution. Bias reduction for all max-domains of attractions, i.e. without restricting to the Pareto-type case, received much less attention up to now. Here we extend the second-order refined POT approach started in Beirlant et al. (2009) providing a bias reduction technique for the classical generalized Pareto (GP) approximation for POTs. We consider parametric and nonparametric modelling of the second order component.