Statistical inference for Sobol pick-freeze Monte Carlo method

Many mathematical models involve input parameters, which are not precisely. Global sensitivity analysis aims to identify the parameters whose 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 of each input variable on the output is the Sobol sensitivity index. consider the statistical estimation of this index from a finite sample of outputs. We study asymptotic and non-asymptotic properties of two of Sobol indices. These properties are applied to significance tests estimation by confidence intervals.