Reducing bias for estimate of population standard deviation

Question

https://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation#Other_distributions

"For non-normal distributions an approximate (up to O(n−1) terms) formula for the unbiased estimator of the standard deviation is: https://wikimedia.org/api/rest_v1/media/math/render/svg/7c03af4ff7000635c861b4e28f7cb99958148333

I would greatly appreciate if somebody can find any reference how this formula above using excess kurtosis is derived? There's lot information about how the correction factor for normal distrubuted populations is derived (n - 1.5): https://www.tandfonline.com/doi/abs/10.1080/00031305.1969.10481865 But how is the version for non-normal distributed populations, using excess kurtosis, derived?

Answer 1

I found an excellent comment by the user Carl Why are we using a biased and misleading standard deviation formula for $\sigma$ of a normal distribution?

However no reference how the formula using excess kurtosis is derived