Generalized Hoeffding-School decomposition for dependent variables - application to sensitivity analysis

In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundness type assumptions on the joint density function of the input variables, we show that a generalized Hoeffding-Sobol decompostion is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices.