Tail and quantile estimation for real-valued β-mixing spatial data

Tchamiè Tchazino , Sophie Dabo-Niang (1) , Aliou Diop

1 MODAL - MOdel for Data Analysis and Learning

This paper deals with extreme-value index estimation of a heavy-tailed distribution of a spatial dependent process. We are particularlyinterested in spatial rare events of a β−mixing process. Given a sta-tionary real-valued multidimensional spatial process {X_i,i ∈ Z^N}, weinvestigate its heavy-tail index estimation. Asymptotic properties ofthe corresponding estimator are established under mildmixingcondi-tions. The particularity of the tail proposed estimator is based on thespatial nature of the sample and its unbiased and reduced variance prop-erties compared to well known tail index estimators. Extreme quantileestimation is also deduced. A numerical study on synthetic and realdatasets is conducted to assess the finite-sample behaviour of the pro-posed estimators.

Mots clés: bias correction; spatial dependence; functional estimation.; Asymptotic normality; β-mixing; extreme value index

Domaines: Statistiques [stat]; Mathématiques [math]

Tchamiè Tchazino, Sophie Dabo-Niang, Aliou Diop. Tail and quantile estimation for real-valued β-mixing spatial data. 2021. ⟨hal-03457114⟩