Talk:Hodges–Lehmann estimator

Extension to multivariate populations
There's this line in the current version:


 * [Hodges–Lehmann estimator] has been generalized from univariate populations to multivariate populations, which produce samples of vectors.

Does anyone have a reference for this? — Preceding unsigned comment added by 174.62.72.221 (talk) 05:18, 12 January 2020 (UTC)

The Cartesian product
Dear friends... If X has n elements, the cardinal of Cartesian product of X×X is $n^2$... So... I guess it should be the set of pairs of two elements.

The Cartesian product
Same here. The statement sounds totally stupid. We have to talk about the set of distinct sets of two elements made of n elements; it's not a Cartesian product. I'll go ahead and fix it.

Vlad Patryshev (talk) 23:21, 12 September 2016 (UTC)

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)


 * You are right. Sorry for reverting. Rracecarr (talk) 14:49, 2 May 2008 (UTC)

Single sample case
The case of the location parameter of a single sample is covered on several web pages and the ones I have seen (e.g. http://www.stat.wmich.edu/s160/book/node11.html) use the formula where a sample value can be paired with itself, as in reverted version of article. I can't find a published direct reference to the named estimate but see page 36 of "Distribution-free statistical methods" by Maritz JS (Chapman&Hall,1981). Melcombe (talk) 12:15, 6 October 2008 (UTC)

Description of the population parameter being estimated in two-sample case is not right
The end of the last sentence of the section on Estimating a population median of a symmetric population says "it estimates the differences between the population of the paired random–variables drawn respectively from the populations". This sentence is mangled. Surely it should be something like "it estimates the median of the population of differences of paired random variables drawn respectively from the two populations.", since the differences of pairs would themselves have a distribution and the two-sample Hodges-Lehmann estimator is going to be estimating some point on that distribution of differences of population-pairs, not the distribution itself. Sample medians converge to population medians, so it stands to reason it will be the median of the distribution of the pair-differences. I don't have the indicated reference handy to check what that says myself, but as it stands, the present sentence doesn't work.

Glenbarnett (talk) 01:06, 15 September 2012 (UTC)

Estimating the population median of a symmetric population
The second paragraph in this section of the present article says "For symmetric distributions, the Hodges–Lehmann statistic has greater efficiency than does the sample median"; however this generalization is false. It's the case for a lot of distributions with a nice broad peak, but is untrue for sufficiently peaked distributions -- the most obvious counterexample is the Laplace distribution but it's true of many other peaky distributions.

Glenbarnett (talk) 23:50, 25 April 2019 (UTC)

Rename “Hodges–Lehmann” to “Hodges-Lehmann”
The title of this page, “Talk:Hodges–Lehmann estimator”, contains an en-dash. Which isn’t even pedantic; it is merely wrong. I propose renaming the page to use a simple hyphen. Objections? (And similar substitutions should be made throughout the page.) JDAWiseman (talk) 12:55, 29 April 2020 (UTC)