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arxiv: 1112.1788 · v3 · pith:CQJD3MJPnew · submitted 2011-12-08 · 🧮 math.ST · stat.TH

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

Ga\"elle Chastaing (M\'ethodes d'Analyse Stochastique des Codes et Traitements Num\'eriques , INRIA Grenoble Rh\^one-Alpes / LJK Laboratoire Jean Kuntzmann) , Fabrice Gamboa (M\'ethodes d'Analyse Stochastique des Codes et Traitements Num\'eriques , IMT) , Cl\'ementine Prieur (M\'ethodes d'Analyse Stochastique des Codes et Traitements Num\'eriques This is my paper
classification 🧮 math.ST stat.TH
keywords variablesinputdecompositiondependentgeneralizedhoeffding-sobolindicesoutput
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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.

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