Project Euclid

In linear models with several observations per cell, a class of estimates of all contrasts are defined in terms of rank test statistics such as the Wilcoxon or normal scores statistic, which extend the results of Hodges and Lehmann (1963) and Lehmann (1963). 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 rank tests on which they are based to the corresponding $t$-tests.