Séance Séminaire

Séminaire de Probabilités et Statistique

Estimating covariate functions associated to multivariate risks: a level sets approach.

The aim of this talk is to study the behavior of a covariate function in a multivariate risks scenario. The first part deals with the problem of estimating the c-upper level sets L(c)={F(x)?c}, with c?(0,1), of an unknown distribution function F on R^d+. . A plug-in approach is followed. We state consistency results with respect to the volume of the symmetric difference and Lp-consistency, with a convergence rate, for the regression function estimate on these level sets L(c). We also consider a new multivariate risk measure: the Covariate-Conditional-Tail-Expectation. We provide a consistent estimator for this measure with a convergence rate. All these results are proven in a non-compact setting. A complete simulation study is detailed. Finally, a real environmental application of our risk measure is provided on waves and water levels in coastal engineering design.These results are exposed in Di Bernardino, Laloë et Servien (2014) accepted in Metrika.