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This question is rather semantic than statistical. In Robust Statistics, estimators of mean and variance of a distribution are often called respectively "estimators of location" and "estimators of scale".The Fisher efficiency of these estimators is said to be maximal when compared to the sample mean of the sample mean or sample variance of the uncontaminated distribution.

What is the point of making a distinction between "estimator of the location" and "estimator of the mean" if these are supposed to be asymptotically the same ?

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  • $\begingroup$ Can you link to an example of this terminology? In robust statistics, an estimator of location is more likely to be a median than a mean. $\endgroup$
    – user225256
    Commented Apr 9, 2021 at 12:18
  • $\begingroup$ @MattF. Sure : researchgate.net/profile/Peter-Rousseeuw/publication/… $\endgroup$
    – outofthegreen
    Commented Apr 12, 2021 at 12:17
  • $\begingroup$ In the publication I sent you above, Rousseeuw is saying that arithmetic mean is the best known estimator for location. $\endgroup$
    – outofthegreen
    Commented Apr 12, 2021 at 12:22
  • $\begingroup$ I think he meant that "of all estimators, the arithmetic mean is the best-known" -- and not "of all known estimators, the arithmetic mean is the best". He talks about estimating the location because he shows the virtue of medians and similar statistics under criteria of robustness. $\endgroup$
    – user225256
    Commented Apr 13, 2021 at 7:41
  • $\begingroup$ @MattF. Yes, I understood that. Still, Rousseeuw defines a location estimate as 100 % efficient if it is the sample mean taken at the uncontaminated distribution, likewise he considers the standard deviation to be a 100% efficient estimate of the scale if this standard deviation is computed on the uncontaminated distribution. Therefore my initial question still stands $\endgroup$
    – outofthegreen
    Commented Apr 13, 2021 at 7:44

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