Among the many estimators of first order Sobol indices that have been proposed in the literature, the so-called rank-based estimator is arguably the simplest to implement. This estimator can be viewed as the empirical auto-correlation of the response variable sample obtained upon reordering the data by increasing values of the inputs. This simple idea can be extended to higher lags of autocorrelation, thus providing several competing estimators of the same parameter. We show that these estimators can be combined in a simple manner to achieve the theoretical variance efficiency bound asymptotically.

翻译：在文献中提出的众多一阶Sobol指数估计量中，所谓的基于排序的估计量可以说是实现最为简单的一种。该估计量可视为将数据按输入值递增顺序重排后，响应变量样本的经验自相关函数。这一简单思想可推广至自相关的高阶滞后项，从而为同一参数提供多个竞争性估计量。我们证明这些估计量可通过简单方式进行组合，以渐近地达到理论方差效率界。