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

Abstract

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 re-ordering the data by increasing values of the inputs. This simple idea can be extended to higher lags of auto-correlation, 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