Efficient estimation of Sobol’ indices of any order from a single input/output sample
Résumé
The main objective of this paper is to estimate optimally Sobol’ indices at any order when a unique input/output i.i.d. sample is available. Our approach stands on three main ingredients: semi-parametric estimation theory, high-order kernel estimation, and mirror-type transformations. We propose two different estimators. We prove that these estimators are asymptotically normal and efficient. Furthermore, we illustrate their numerical properties on standard examples.
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main_2024_10_16.pdf (546.16 Ko)
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SupplementalMaterialHighOrderKernels.pdf (339.92 Ko)
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