Efficient Estimation of Nonlinear Conditional Functionals of a Density

Sébastien da Veiga (1, 2, 3) , Fabrice Gamboa (1, 3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IFPEN - IFP Energies nouvelles
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

In this paper we address the problem of estimating functional integrals of conditional moments of the form $\E(\psi(\E(\varphi(Y)|X)))$ where $(X,Y)$ is a random vector with joint density $f$ and $\psi$ and $\varphi$ are functions that are differentiable enough. This problem is motivated by the asymptotically efficient estimation of Sobol sensitivity indices.

Mots clés: Density Estimation; semiparametric Cramér-Rao bound; global sensitivity analysis

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Sébastien da Veiga, Fabrice Gamboa. Efficient Estimation of Nonlinear Conditional Functionals of a Density. 2008. ⟨hal-00266110v1⟩