In the estimation of a location parameter the Hodges-Lehmann estimator is known to have some "robust" properties, but it is very "expensive" for large sample sizes. By using the linearity of a special rank statistic we can find a linearized version which requires only $O(n \log n)$ operations.
"A Linearized Version of the Hodges-Lehmann Estimator." Ann. Statist. 2 (6) 1308 - 1313, November, 1974. https://doi.org/10.1214/aos/1176342883