Estimation of the Sobol indices in a linear functional multidimensional model

Jean-Claude Fort (1) , Thierry Klein (2) , Agnès Lagnoux (2) , Béatrice Laurent (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider a functional linear model where the explicative variables are stochastic processes taking values in a Hilbert space, the main example is given by Gaussian processes in L2([0; 1]). We propose estimators of the Sobol indices in this functional linear model. Our estimators are based on Ustatistics. We prove the asymptotic normality and the efficiency of our estimators and we compare them from a theoretical and practical point of view with classical estimators of Sobol indices.

Mots clés: Karhunen-Loève expansion; fractional Gaussian process; semiparametric efficient estimation; sensitivity analysis; quadratic functionals

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

Jean-Claude Fort, Thierry Klein, Agnès Lagnoux, Béatrice Laurent. Estimation of the Sobol indices in a linear functional multidimensional model. Journal of Statistical Planning and Inference, 2013, 143 (9), pp.1590-1605. ⟨hal-00685998⟩