# Asymptotic normality and efficiency of two Sobol index estimators

Alexandre Janon; Thierry Klein; Agnès Lagnoux; Maëlle Nodet; Clémentine Prieur

ESAIM: Probability and Statistics (2014)

- Volume: 18, page 342-364
- ISSN: 1292-8100

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topJanon, Alexandre, et al. "Asymptotic normality and efficiency of two Sobol index estimators." ESAIM: Probability and Statistics 18 (2014): 342-364. <http://eudml.org/doc/273644>.

@article{Janon2014,

abstract = {Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and state a central limit theorem for each. We show that one of these estimators has an optimal asymptotic variance. We also generalize our results to the case where the true output is not observable, and is replaced by a noisy version.},

author = {Janon, Alexandre, Klein, Thierry, Lagnoux, Agnès, Nodet, Maëlle, Prieur, Clémentine},

journal = {ESAIM: Probability and Statistics},

keywords = {sensitivity analysis; sobol indices; asymptotic efficiency; asymptotic normality; confidence intervals; metamodelling; surface response methodology; Sobol indices},

language = {eng},

pages = {342-364},

publisher = {EDP-Sciences},

title = {Asymptotic normality and efficiency of two Sobol index estimators},

url = {http://eudml.org/doc/273644},

volume = {18},

year = {2014},

}

TY - JOUR

AU - Janon, Alexandre

AU - Klein, Thierry

AU - Lagnoux, Agnès

AU - Nodet, Maëlle

AU - Prieur, Clémentine

TI - Asymptotic normality and efficiency of two Sobol index estimators

JO - ESAIM: Probability and Statistics

PY - 2014

PB - EDP-Sciences

VL - 18

SP - 342

EP - 364

AB - Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and state a central limit theorem for each. We show that one of these estimators has an optimal asymptotic variance. We also generalize our results to the case where the true output is not observable, and is replaced by a noisy version.

LA - eng

KW - sensitivity analysis; sobol indices; asymptotic efficiency; asymptotic normality; confidence intervals; metamodelling; surface response methodology; Sobol indices

UR - http://eudml.org/doc/273644

ER -

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