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Asymptotic normality and efficiency of two Sobol index estimators

Alexandre Janon, Thierry Klein, Agnès Lagnoux, Maëlle Nodet, Clémentine Prieur (2014)

ESAIM: Probability and Statistics

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...

Asymptotic normality of the integrated square error of a density estimator in the convolution model.

Cristina Butucea (2004)

SORT

In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not fixed, the results hold for any sequence of bandwidths decreasing to 0. In particular the central limit...

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