Hodges-Lehmann Estimator

The Hodges-Lehmann estimator is a robust, nonparametric estimator of the location, or central value, of a population, developed as an alternative to the ordinary sample mean or median. For a population with a symmetric distribution, such as the normal distribution or the Student's t-distribution, it gives a consistent, median-unbiased estimate of the population's median; for a population that is not symmetric, it instead estimates a related quantity called the pseudo-median. Originally defined for a single one-dimensional population, it has since been extended to estimate the difference between two populations and to multivariate data producing vector-valued samples. Built on the Wilcoxon signed-rank statistic, it was proposed independently in 1963 by Pranab Kumar Sen and by Joseph Hodges and Erich Lehmann, and is sometimes called the Hodges-Lehmann-Sen estimator, standing as an early and influential example of a rank-based estimator in nonparametric and robust statistics.