Hodges-Lehmann Estimators for non-Wilcoxon cases

[AllenFleishman]

Can one easily compute Hodges-Lehmann Estimators for statistics other than the Wilcoxon test?  For example, for paired data or sign-test?

[SteveDenham]

A quick test on some data at hand says it will take some major work with output to get the HL estimators.  I couldn't get them for anything other than the Wilcoxon test.

Steve Denham

[AllenFleishman]

Thank you Steve, too bad that SAS cannot copy the R code which is available (e.g., R Graphical Manual).

On another two observations on the Hodges-Lehmann estimators,

1. I discovered that when the Wilcoxon p-value is just barely statistically significant (e.g., 0.045 when N/group = 6), then the HL estimators do not always exclude 0.  This was confirmed by the SAS developer.  A SAS consultant and a 2011 talk by Riji Yao, et. al. suggested that either an Exact solution or a sampling approach might yield HL estimators which are consistent with the p-values.
2. A Monte Carlo study observed across a range of distributions that the t-test CI gives about 21% narrower CI than the HL when N is small.  Only for leptokurtic distributions and large Ns might the HL offer a slightly smaller CI.  Although with the central limit theorem, the distribution of means very, very quickly converge on normal, questioning the underlying need for non-parametric approaches.