Hodges–Lehmann estimator

Summary

The Hodges–Lehmann estimator estimates the centre of a symmetric distribution by the median of all pairwise averages of the observations. It is the estimator that corresponds to the Wilcoxon signed-rank test, and it inherits its good properties. It resists outliers much better than the mean, and for normal data it is almost as precise, with asymptotic relative efficiency $3/\pi \approx 0.955$. A two-sample version estimates a shift between two populations by the median of all pairwise differences.