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Is it a good idea to use Huber, Tukey or similar weighting function for estimating robust mean? What are the advantages/disadvantages of using such an estimate vs. using median (I am particularly interested in the robustness: breakdown point, sensitivity to different types of outliers, etc.).

Roger Vadim
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    Does this answer your question? [Tradeoffs of robust mean measures (trimmed, Huber, cosh, etc)](https://stats.stackexchange.com/questions/373067/tradeoffs-of-robust-mean-measures-trimmed-huber-cosh-etc) – jbowman Mar 09 '20 at 13:43
  • Although not an exact duplicate of https://stats.stackexchange.com/questions/373067/tradeoffs-of-robust-mean-measures-trimmed-huber-cosh-etc?rq=1, the latter does basically answer the question. – jbowman Mar 09 '20 at 13:44
  • @jbowman thanks, it certainly helps. However, I hope for a more quantitative answers, such comparison of the breakdown points, sensitivity to different types of outliers, etc. – Roger Vadim Mar 09 '20 at 13:49
  • +1 This looks like a better version of your previous question. – whuber Mar 09 '20 at 14:29
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    Ah, OK, it might be helpful if you edited your question to include your request for information about breakpoints, sensitivities, etc. directly in the question instead of just in the comments. I'm retracting my close vote, sorry about that. – jbowman Mar 09 '20 at 15:30
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    This is a fair question, but the answer is at least a chapter if not several in any text on robust statistics, and there is a spectrum of opinion beyond that. I think it is still too broad, although as @whuber comments it's better than the previous version. Footnote: our William Huber $\ne$ Peter J. Huber, implied in the title and text. – Nick Cox Mar 09 '20 at 15:54
  • I appreciate the fact that simple questions are often not as simple as they seem. In my case it is a part of a bigger problem, and spending too much time on studying statistical literature is not an option (although it could be an exciting endeavor). I am looking for the basic facts that would help me to identify and (hopefully) bypass the failure of my estimator. – Roger Vadim Mar 09 '20 at 17:05
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    It's really hard to say. There is no precise information here about your data. But in general most robust alternatives to the mean will give you results somewhere between the mean and median. – Nick Cox Mar 09 '20 at 17:28

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