  In this paper we address the problem of efficient estimation of Sobol
sensitivy indices. First, we focus on general 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. In particular, we show that asymptotical
efficient estimation of this functional boils down to the estimation of crossed
quadratic functionals. An efficient estimate of first-order sensitivity indices
is then derived as a special case. We investigate its properties on several
analytical functions and illustrate its interest on a reservoir engineering
case.
