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

The objective of the present work is to estimate Sobol’ indices at any order in a given-data context, where a unique input/output sample is available. In that view, our approach consists of three main ingredients: one-step inference and nonpositive kernel estimation following [1] together with mirrortype transformations as introduced in [2,3]. We introduce two different estimators that are proved to be asymptotically normal and efficient. In addition, their numerical properties are illustrated on standard examples.

References:

[1] K. Doksum and A. Samarov. Nonparametric estimation of global functionals and a measure of the explanatory power of covariates in regression. The Annals of Statistics, 1443–1473, 1995.

[2] K. Bertin, N. Klutchnikoff, J. R. León, and C. Prieur. Adaptive density estimation on bounded domains under mixing conditions. Electronic Journal of Statistics, 14(1):2198–2237, 2020.

[3] L. Pujol. Nonparametric estimation of a multivariate density under kullback-leibler loss with ISDE. arXiv preprint arXiv:2205.03199, 2022.

Joint work with: Sébastien Da Veiga; Univ Rennes, Ensai, CNRS, CREST ; Fabrice Gamboa, Thierry Klein and Agnes Lagnoux; Institut de Mathématiques de Toulouse.