Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory

Elena Di Bernadino (1) , Thomas Laloë (2) , Véronique Maume-Deschamps (1) , Clémentine Prieur (3)

1 SAF - Laboratoire de Sciences Actuarielle et Financière
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 MOISE - Modelling, Observations, Identification for Environmental Sciences

This paper deals with the problem of estimating the level sets of an unknown distribution function $F$. A plug-in approach is followed. That is, given a consistent estimator $F_n$ of $F$, we estimate the level sets of $F$ by the level sets of $F_n$. In our setting no compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by applications in multivariate risk theory. In this sense we also present simulated and real examples which illustrate our theoretical results.

Mots clés: Level sets; Distribution function; Plug-in estimation; Hausdorff distance; Conditional Tail Expectation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Gestion des risques [q-fin.RM]

Elena Di Bernadino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur. Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory. 2011. ⟨hal-00580624v1⟩