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Pré-Publication, Document De Travail Année : 2023

New estimation of Sobol' indices using kernels

Résumé

In this work, we develop an approach mentioned by da Veiga and Gamboa in 2013. It consists in extending the very interesting point of view introduced in \cite{gine2008simple} to estimate general nonlinear integral functionals of a density on the real line, by using empirically a kernel estimator erasing the diagonal terms. Relaxing the positiveness assumption on the kernel and choosing a kernel of order large enough, we are able to prove a central limit theorem for estimating Sobol' indices of any order (the bias is killed thanks to this signed kernel).
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Dates et versions

hal-04052837 , version 1 (30-03-2023)

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Sébastien Da Veiga, Fabrice Gamboa, Agnès Lagnoux, Thierry Klein, Clémentine Prieur. New estimation of Sobol' indices using kernels. 2023. ⟨hal-04052837⟩
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