2018/03/08 by Maikol Solís, Solís, Maikol · 2 citations
Decision Sciences · Mathematics · #62F40 #62G08 #93B35 #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1803.03333
openalex publication_date 2018/03/08 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Suppose that Y = \ψ(X1, \…, Xp), where (X1,\…, Xp)^ top are\nrandom inputs, Y is the output, and \ψ(\⋅) is an unknown link\nfunction. The Sobol indices gauge the sensitivity of each X against Y by\nestimating the regression curve's variability between them. In this paper, we\nestimate these curves with a kernel-based method. The method allows to estimate\nthe first order indices when the link between the independent and dependent\nvariables is unknown. The kernel-based methods need a bandwidth to average the\nobservations. For finite samples, the cross-validation method is famous to\ndecide this bandwidth. However, it produces a structural bias. To remedy this,\nwe propose a bootstrap procedure which reconstruct the model residuals and\nre-estimate the non-parametric regression curve. With the new set of curves,\nthe procedure corrects the bias in the Sobol index. To test the developed\nmethod, we implemented simulated numerical examples with complex functions.\n