For a continuous and diagonally symmetric multivariate distribution, incorporating the idea of preliminary test estimators, a variant form of the James-Stein type estimation rule is used to formulate some shrinkage estimators of location based on rank statistics and $U$-statistics. In an asymptotic setup, the relative risks for these shrinkage estimators are shown to be smaller than their classical counterparts.
"On Some Shrinkage Estimators of Multivariate Location." Ann. Statist. 13 (1) 272 - 281, March, 1985. https://doi.org/10.1214/aos/1176346592