Talk:Hodges-Lehmann estimator
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[edit] What is estimated?
(in response to questions raised on the reason for edit line)
The estimator is a consistent estimator of something definite, but something that is a property of some distribution function that that is derived from the distribution functions of the different data sets. For the two-sample case the derived distribution is that of the difference between samples from the two original distributions. Since the original distributions can be anything, the derived distribution will not generally be symmetric and hence the median of the differences is not the same as the mean of the differences. Further the median of the distribution of the differences is not the same as the difference between the medians of the original distributions ... there is no one-to-one correspondence. Note that these are a properties of the population distributions and do not involve sampling properties at all. The H-L estimator estimates the median of the differences. Melcombe (talk) 13:47, 2 May 2008 (UTC)
