Conditional extremes from heavy-tailed distributions: An application to the estimation of extreme rainfall return levels

Laurent Gardes (1) , Stéphane Girard (1)

1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems

This paper is dedicated to the estimation of extreme quantiles and the tail index from heavy-tailed distributions when a covariate is recorded simultaneously with the quantity of interest. A nearest neighbor approach is used to construct our estimators. Their asymptotic normality is established under mild regularity conditions and their finite sample properties are illustrated on a simulation study. An application to the estimation of pointwise return levels of extreme rainfalls in the Cevennes-Vivarais region is provided.

Keywords: Conditional extreme quantiles; heavy-tailed distribution; nearest neighbor estimator; extreme rainfalls.; extreme rainfalls

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]

Laurent Gardes, Stéphane Girard. Conditional extremes from heavy-tailed distributions: An application to the estimation of extreme rainfall return levels. Extremes, 2010, 13 (2), pp.177-204. ⟨10.1007/s10687-010-0100-z⟩. ⟨hal-00371757v4⟩