Risk of estimators for Sobol’ sensitivity indices based on metamodels

Sobol' sensitivity indices allow to quantify the respective effects of random input variables and their combinations on variance mathematical model output. We focus problem estimation via a metamodeling approach where we replace true with sample-based approximation compute indices. propose new method for quality control obtain asymptotic non-asymptotic risk bounds estimates based general class metamodels. Our analysis is closely connected nonparametric function fitting using orthogonal system functions in design setting. It considers relation between metamodel error corresponding estimator shows possibility fast convergence rates case noiseless observations. The theoretical results are complemented numerical experiments approximations multivariate Legendre Trigonometric polynomials.