SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 2, Page 693-716, January 2020.
The Shapley effects are global sensitivity indices: they quantify the impact of each input variable on the output variable in a model. In this work, we suggest new estimators of these sensitivity indices. When the input distribution is known, we investigate the already existing estimator defined in [E. Song, B. L. Nelson, and J. Staum, SIAM/ASA J. Uncertain. Quantif., 4 (2016), pp. 1060--1083] and suggest a new one with a lower variance. Then, when the distribution of the inputs is unknown, we extend these estimators. We provide asymptotic properties of the estimators studied in this article. We also apply one of these estimators to a real data set.

中文翻译：

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估计Shapley效应并适应未知输入分布的方差降低

SIAM / ASA不确定性量化杂志，第8卷，第2期，第693-716页，2020年1月。Shapley
效应是全局敏感性指数：它们量化模型中每个输入变量对输出变量的影响。在这项工作中，我们建议对这些敏感性指数进行新的估算。当输入分布已知时，我们将研究[E.中定义的已经存在的估计量。Song，BL Nelson和SIAM / ASA的J.Staum J.不确定。Quantif。，4（2016），pp。1060--1083]，并提出了一种方差较低的新方法。然后，当输入的分布未知时，我们扩展这些估计量。我们提供本文研究的估计量的渐近性质。我们还将这些估计器之一应用于真实数据集。