Preprints, Working Papers, ... Year : 2024

Efficient estimation of Sobol’ indices of any order from a single input/output sample

Abstract

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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Dates and versions

hal-04052837 , version 1 (30-03-2023)
hal-04052837 , version 2 (16-10-2024)

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Sébastien Da Veiga, Fabrice Gamboa, Agnès Lagnoux, Thierry Klein, Clémentine Prieur. Efficient estimation of Sobol’ indices of any order from a single input/output sample. 2024. ⟨hal-04052837v2⟩
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