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2014 Sensitivity analysis for multidimensional and functional outputs
Fabrice Gamboa, Alexandre Janon, Thierry Klein, Agnès Lagnoux
Electron. J. Statist. 8(1): 575-603 (2014). DOI: 10.1214/14-EJS895


Let $X:=(X_{1},\ldots,X_{p})$ be random objects (the inputs), defined on some probability space $(\Omega,\mathcal{F},\mathbb{P})$ and valued in some measurable space $E=E_{1}\times\ldots\times E_{p}$. Further, let $Y:=Y=f(X_{1},\ldots,X_{p})$ be the output. Here, $f$ is a measurable function from $E$ to some Hilbert space $\mathbb{H}$ ($\mathbb{H}$ 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 $Y\in\mathbb{R}$), when the output belongs to $\mathbb{H}$. These indices have 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 asymptotic behaviour of such an estimation scheme.


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Fabrice Gamboa. Alexandre Janon. Thierry Klein. Agnès Lagnoux. "Sensitivity analysis for multidimensional and functional outputs." Electron. J. Statist. 8 (1) 575 - 603, 2014.


Published: 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1348.62106
MathSciNet: MR3211025
Digital Object Identifier: 10.1214/14-EJS895

Primary: 62G05 , 62G20

Keywords: Concentration inequalities , quadratic functionals , Semi-parametric efficient estimation , sensitivity analysis , Sobol indices , temporal output , vector output

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.8 • No. 1 • 2014
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