Journal
ELECTRONIC JOURNAL OF STATISTICS
Volume 8, Issue -, Pages 575-603Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/14-EJS895
Keywords
Semi-parametric efficient estimation; sensitivity analysis; quadratic functionals; Sobol indices; vector output; temporal output; concentration inequalities
Categories
Funding
- French National Research Agency (ANR) through COSINUS program (COSTA-BRAVA) [ANR-09-COSI-015]
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Let X := (X-1, . . . , X-p be random objects (the inputs), defined on some probability space (Omega, F, P) and valued in some measurable space E = E-1 x . . . x Ep. Further, let Y := Y = f(X-1,...,Xp) be the output. Here, f is a measurable function from E to some Hilbert space H (H could be either of finite or infinite dimension). In this work, we give a natural generalization of the Sobol indices (that are classically defined when Y is an element of R), when the output belongs to H. These indices ham very nice properties. First, they are invariant under isometry and scaling. Further they can be, as in dimension 1, easily estimated by using the so-called Pick and Freeze method. We investigate the asympotic behaviour of such an estimation scheme.
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