  In this paper, we address the estimation of the sensitivity indices called
"Shapley eects". These sensitivity indices enable to handle dependent input
variables. The Shapley eects are generally dicult to estimate, but they are
easily computable in the Gaussian linear framework. The aim of this work is to
use the values of the Shapley eects in an approximated Gaussian linear
framework as estimators of the true Shapley eects corresponding to a non-linear
model. First, we assume that the input variables are Gaussian with small
variances. We provide rates of convergence of the estimated Shapley eects to
the true Shapley eects. Then, we focus on the case where the inputs are given
by an non-Gaussian empirical mean. We prove that, under some mild assumptions,
when the number of terms in the empirical mean increases, the dierence between
the true Shapley eects and the estimated Shapley eects given by the Gaussian
linear approximation converges to 0. Our theoretical results are supported by
numerical studies, showing that the Gaussian linear approximation is accurate
and enables to decrease the computational time signicantly.
