Robust estimators suggested by Hodges and Lehmann in 1963. The estimate of location for a sample of n observations is the median of the averages of the ½ n(n−1) possible pairs of observations. For example, with the four observations 22, 24, 26, and 60, the six possible averages are 23, 24, 41, 25, 42 and 43, so that the Hodges–Lehmann location estimate is 33 (equal to the mean in this case).
In the case of samples (of sizes m and n) from two populations, where an estimate is required of the difference in their locations, the Hodges–Lehmann estimate is the median of the mn possible differences resulting from taking one observation from each sample.
Subjects: Probability and Statistics.