  In this work, we develop an approach mentioned by da Veiga and Gamboa in
2013. It consists in extending the very interestingpoint of view introduced in
\cite{gine2008simple} to estimate general nonlinear integral functionals of a
density on the real line, by using empirically a kernel estimator erasing the
diagonal terms. Relaxing the positiveness assumption on the kernel and choosing
a kernel of order large enough, we are able to prove a central limit theorem
for estimating Sobol' indices of any order (the bias is killed thanks to this
signed kernel).
