Local robust estimation of the Pickands dependence function

Mikael Escobar-Bach (1) , Yuri Goegebeur (1) , Armelle Guillou (2)

1 IMADA - Department of Mathematics and Computer Science [Odense]
2 IRMA - Institut de Recherche Mathématique Avancée

We consider the robust estimation of the Pickands dependence function in the random covariate framework. Our estimator is based on local estimation with the minimum density power divergence criterion. We provide the main asymptotic properties, in particular the convergence of the stochastic process, correctly normalized, towards a tight centered Gaussian process. The finite sample performance of our estimator is evaluated with a simulation study involving both uncontaminated and contaminated samples. The method is illustrated on a dataset of air pollution measurements.

Mots clés: Conditional Pickands dependence function; robustness; stochastic convergence

Domaines: Statistiques [math.ST]

Mikael Escobar-Bach, Yuri Goegebeur, Armelle Guillou. Local robust estimation of the Pickands dependence function. Annals of Statistics, 2018, 46, pp.2806-2843. ⟨10.1214/17-AOS1640⟩. ⟨hal-01340166v3⟩