I am looking for an accessible review of the breakdown properties of the median (estimator of location) and possible practical solutions for dealing with it.

(By accessible I mean short and readable by a non-statistician, although at ease with math. If you can review the main points in the answer's section, it could be sufficient.)

  • $\begingroup$ Could you please clarify what you mean by "dealing with it"? $\endgroup$ – whuber Mar 8 '20 at 13:27
  • $\begingroup$ Robust estimation of a sample mean is a part of a bigger algorithm that I am working on. I have identified some obvious cases where it breaks down - e.g., when I have only one good data point and one outlier (whereas everything else is missing data). I however would like to have a more general solution for less obvious cases. $\endgroup$ – Vadim Mar 8 '20 at 13:31
  • $\begingroup$ Are you asking about the mean or the median? They are different properties and, unless you make special assumptions, usually have different estimators. $\endgroup$ – whuber Mar 8 '20 at 13:33
  • $\begingroup$ There are actually two estimators there: one is simple median, the other is using Huber weight. $\endgroup$ – Vadim Mar 8 '20 at 13:35
  • 2
    $\begingroup$ Yes, for over 30 years in hundreds of cases--but why does it matter? $\endgroup$ – whuber Mar 8 '20 at 19:08

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