A kernel estimate method for characteristic function-based uncertainty importance measure

In this paper, we propose a fast computation method based on a kernel function for the characteristic function-based moment-independent uncertainty importance measure θ_i. We first point out that the possible computational complexity problems that exist in the estimation of θ_i. Since the convergence rate of a double-loop Monte Carlo (MC) simulation is O(N^−1/4), the first possible problem is the use of double-loop MC simulation. And because the norm of the difference between the unconditional and conditional characteristic function of model output in θ_i is a Lebesgue integral over the infinite interval, another possible problem is the computation of this norm. Then a kernel function is introduced to avoid the use of double-loop MC simulation, and a longer enough bounded interval is selected to instead of the infinite interval to calculate the norm. According to these improvements, a kind of fast computational methods is introduced for θ_i, and during the whole process, all θ_i can be obtained by using a single quasi-MC sequence. From the comparison of numerical error analysis, it can be shown that the proposed method is an effective and helpful approach for computing the characteristic function-based moment-independent importance index θ_i.