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

• Published in: Applied mathematical modelling Vol. 42; pp. 58 - 70
• Main Authors: Xu, Xin, Lu, Zhenzhou, Luo, Xiaopeng
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2017
• Subjects: Characteristic function; Kernel estimate method; Moment-independent; Uncertainty importance analysis; Characteristic function; Uncertainty importance analysis; Kernel estimate method; Moment-independent
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2016.09.028

•A fast computational method is proposed for the characteristic function (CF)-based measure.•The possible computational complexity problems are analyzed for the CF-based index.•A kernel estimate is introduced to avoid the double-loop MC simulation.•An interval-truncation approach is introduced to calculate the norm of characteristic functions. In this paper, we propose a fast computation method based on a kernel function for the characteristic function-based moment-independent uncertainty importance measure θi. We first point out that the possible computational complexity problems that exist in the estimation of θi. 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 θi 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 θi, and during the whole process, all θi 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 θi.