Efficient Estimation of Sensitivity Indices

Details Efficient Estimation of Sensitivity Indices Efficient Estimation of Sensitivity Indices

2012-03-13

arxiv.org/abs/1203.2899v1

Mathematics

Statistics Theory

41 pages

Scientific paper

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.

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