In linear models with several observations per cell, estimates of all contrasts are given whose small and large sample behaviour is analogous to that of the estimate of a shift parameter proposed in . In particular, the asymptotic efficiency of these estimates relative to the standard least squares estimates, as the number of observations in each cell gets large, is shown to be the same as the Pitman efficiency of the Wilcoxon test relative to the $t$-test.
"Robust Estimation in Analysis of Variance." Ann. Math. Statist. 34 (3) 957 - 966, September, 1963. https://doi.org/10.1214/aoms/1177704018