Electronic Journal of Statistics

Sensitivity analysis for multidimensional and functional outputs

Fabrice Gamboa, Alexandre Janon, Thierry Klein, and Agnès Lagnoux

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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.

Article information

Electron. J. Statist., Volume 8, Number 1 (2014), 575-603.

First available in Project Euclid: 20 May 2014

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Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G20: Asymptotic properties

Semi-parametric efficient estimation sensitivity analysis quadratic functionals Sobol indices vector output temporal output concentration inequalities


Gamboa, Fabrice; Janon, Alexandre; Klein, Thierry; Lagnoux, Agnès. Sensitivity analysis for multidimensional and functional outputs. Electron. J. Statist. 8 (2014), no. 1, 575--603. doi:10.1214/14-EJS895. https://projecteuclid.org/euclid.ejs/1400592265

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