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I'm looking for an unbiased estimator of the standard deviation $\text{SD}(s)$ of the sample standard deviation $s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \overline{x})^2}$. I have found this answer which is highly relevant to this question, however, I would prefer a solution that does not assume normality (similarly to the unbiased estimator of the variance of the sample variance).

Is there a general solution for non-normal distributions?

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  • $\begingroup$ Probably for particular families of distributions there are such estimators but for all probability distributions in general, or even for all with finite moments, I suspect there is none. $\endgroup$
    – Michael Hardy
    Commented Apr 22, 2019 at 23:58
  • $\begingroup$ My impression is that we either have yet to find one that works as broadly as $S^2$ does for variance (e.g., specific to the normal distribution) or that we have shown that no such estimator can exist. I am, however, unsure which of those is correct. $\endgroup$
    – Dave
    Commented Jun 9, 2021 at 18:03

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