Bias correction in conditional multivariate extremes

Mikael Escobar-Bach (1) , Yuri Goegebeur (2) , Armelle Guillou (3)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 IMADA - Department of Mathematics and Computer Science [Odense]
3 IRMA - Institut de Recherche Mathématique Avancée

We consider bias-corrected estimation of the stable tail dependence function in the regression context. To this aim, we first estimate the bias of a smoothed estimator of the stable tail dependence function, and then we subtract it from the estimator. The weak convergence, as a stochastic process, of the resulting asymptotically unbiased estimator of the conditional stable tail dependence function, correctly normalized, is established under mild assumptions, the covariate argument being fixed. The finite sample behaviour of our asymptotically unbiased estimator is then illustrated on a simulation study and compared to two alternatives, which are not bias corrected. Finally, our methodology is applied to a dataset of air pollution measurements.

Mots clés: Bias correction; conditional stable tail dependence function; stochastic convergence

Domaines: Statistiques [math.ST]

Mikael Escobar-Bach, Yuri Goegebeur, Armelle Guillou. Bias correction in conditional multivariate extremes. Electronic Journal of Statistics , 2020, 14, pp.1773-1795. ⟨10.1214/20-EJS1706⟩. ⟨hal-01887925⟩