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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.).

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    $\begingroup$ Does this answer your question? Tradeoffs of robust mean measures (trimmed, Huber, cosh, etc) $\endgroup$
    – jbowman
    Mar 9, 2020 at 13:43
  • $\begingroup$ Although not an exact duplicate of stats.stackexchange.com/questions/373067/…, the latter does basically answer the question. $\endgroup$
    – jbowman
    Mar 9, 2020 at 13:44
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    $\begingroup$ 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. $\endgroup$
    – jbowman
    Mar 9, 2020 at 15:30
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    $\begingroup$ 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. $\endgroup$
    – Nick Cox
    Mar 9, 2020 at 15:54
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    $\begingroup$ 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. $\endgroup$
    – Nick Cox
    Mar 9, 2020 at 17:28

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