# Unbiased Estimator of the Standard Deviation of the Sample Standard Deviation

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?

• 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. Apr 22, 2019 at 23:58
• 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.
– Dave
Jun 9, 2021 at 18:03