Local estimation of the conditional stable tail 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 local estimation of the stable tail dependence function when a random covariate is observed together with the variables of main interest. Our estimator is a weighted version of the empirical estimator adapted to the covariate framework. We provide the main asymptotic properties of our estimator, when properly normalized, in particular the convergence of the empirical process towards a tight centered Gaussian process. The finite sample performance of our estimator is illustrated on a small simulation study and on a dataset of air pollution measurements.

Mots clés: Conditional stable tail dependence function; empirical process; stochastic convergence

Domaines: Statistiques [math.ST]

Mikael Escobar-Bach, Yuri Goegebeur, Armelle Guillou. Local estimation of the conditional stable tail dependence function. Scandinavian Journal of Statistics, 2018, 45, pp.590-617. ⟨10.1111/sjos.12315⟩. ⟨hal-01382204v2⟩