0

In this post, an unbiased estimator for the standard deviation of the standard deviation under normality is provided. I would be interested in such an estimator without the normality assumption, i.e., the standard deviation of the standard deviation for arbitrary distributions.

Hiro
  • 303
  • 2
    I believe such an estimator has been shown not to exist! – Dave Nov 21 '23 at 12:14
  • 1
    I see. It would be great if someone can provide a reference to Dave's statement. – Hiro Nov 21 '23 at 12:58
  • Because the bias depends on (at least) the fourth moment of the distribution and there are many distributions with the same SD but different fourth moment, Dave's claim follows easily. – whuber Nov 21 '23 at 16:55
  • @whuber What if the 4th moment doesn’t exist? – Dave Nov 21 '23 at 17:00
  • @Dave I leave it to you to answer that question yourself, because we don't need to consider that possibility: the logic of my comment continues to apply when we limit the scope of "arbitrary distributions" to those with finite fourth moments. – whuber Nov 21 '23 at 17:02
  • @whuber Ok, but shouldn't it be possible to derive an estimator that takes the (sample) fourth moment (for distributions with finite fourth moments) into account to correct the bias introduced by the normality assumption? – Hiro Nov 21 '23 at 17:36
  • 1
    See the discussion at https://stats.stackexchange.com/questions/249688. – whuber Nov 21 '23 at 18:16

0 Answers0