Title: Metamodel Construction for Sensitivity Analysis,
Abstract: We propose to estimate a metamodel and the sensitivity indices of a complex
model m in the Gaussian regression framework. Our approach combines methods for
sensitivity analysis of complex models and statistical tools for sparse
non-parametric estimation in multivariate Gaussian regression model. It rests
on the construction of a metamodel for aproximating the Hoeffding-Sobol
decomposition of m. This metamodel belongs to a reproducing kernel Hilbert
space constructed as a direct sum of Hilbert spaces leading to a functional
ANOVA decomposition. The estimation of the metamodel is carried out via a
penalized least-squares minimization allowing to select the subsets of
variables that contribute to predict the output. It allows to estimate the
sensitivity indices of m. We establish an oracle-type inequality for the risk
of the estimator, describe the procedure for estimating the metamodel and the
sensitivity indices, and assess the performances of the procedure via a
simulation study.