Generalized Hoeffding-Sobol Decomposition for Dependent Variables - Application to Sensitivity Analysis

Gaëlle Chastaing (1, 2) , Fabrice Gamboa (1, 3) , Clémentine Prieur (1, 2)

1 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
2 MOISE - Modelling, Observations, Identification for Environmental Sciences
3 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices.

Mots clés: Sensitivity analysis; Hoeffding decomposition; Dependent variables

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Gaëlle Chastaing, Fabrice Gamboa, Clémentine Prieur. Generalized Hoeffding-Sobol Decomposition for Dependent Variables - Application to Sensitivity Analysis. Electronic Journal of Statistics , 2012, 6, pp.2420-2448. ⟨10.1214/12-EJS749⟩. ⟨hal-00649404v3⟩