1
$\begingroup$

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.

Improve this question
$\endgroup$
7
  • 3
    $\begingroup$ I believe such an estimator has been shown not to exist! $\endgroup$
    – Dave
    Commented Nov 21, 2023 at 12:14
  • 1
    $\begingroup$ I see. It would be great if someone can provide a reference to Dave's statement. $\endgroup$
    – Hiro
    Commented Nov 21, 2023 at 12:58
  • 1
    $\begingroup$ 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. $\endgroup$
    – whuber ♦
    Commented Nov 21, 2023 at 16:55
  • $\begingroup$ @whuber What if the 4th moment doesn’t exist? $\endgroup$
    – Dave
    Commented Nov 21, 2023 at 17:00
  • 2
    $\begingroup$ See the discussion at stats.stackexchange.com/questions/249688. $\endgroup$
    – whuber ♦
    Commented Nov 21, 2023 at 18:16

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.