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

Efficiency of the averaged rank-based estimator for first order Sobol index inference