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?

  • $\begingroup$ 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 Apr 22 at 23:58

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