Linking the Hoeffding--Sobol and Möbius formulas through a decomposition of Kuo, Sloan, Wasilkowski, and Wozniakowski

Cécile Mercadier (1) , Olivier Roustant (2) , Christian Genest (3)

1 PSPM - Probabilités, statistique, physique mathématique
2 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse
3 Department of Mathematics and Statistics McGill University

Extensions of a result of Kuo et al. (Math. Comp., 79 (2010), 953–966) are presented which unify the derivation of the Hoeffding--Sobol and Möbius decompositions of a multivariate function as a sum of terms of increasing complexity.

Mots clés: Möbius decomposition; Hoeffding--Sobol decomposition; Functional representation

Domaines: Statistiques [math.ST]

Cécile Mercadier, Olivier Roustant, Christian Genest. Linking the Hoeffding--Sobol and Möbius formulas through a decomposition of Kuo, Sloan, Wasilkowski, and Wozniakowski. Statistics and Probability Letters, 2022, 185, pp.109419. ⟨10.1016/j.spl.2022.109419⟩. ⟨hal-03220809v3⟩