Orthogonal arrays for estimating global sensitivity indices of non-parametric models based on ANOVA high-dimensional model representation

Global sensitivity indices play important roles in global sensitivity analysis based on ANOVA high-dimensional model representation. However, few effective methods are available for the estimation of the indices when the objective function is a non-parametric model. In this paper, we explore the estimation of global sensitivity indices of non-parametric models. The main result (Theorem 2.1) shows that orthogonal arrays (OAs) are A-optimality designs for the estimation of Θ _M, the definition of which can be seen in Section 1. Estimators of global sensitivity indices are proposed based on orthogonal arrays and proved to be accurate for small indices. The performance of the estimators is illustrated by a simulation study.