# Thread: Standard error of the sample standard deviation

1. ## Standard error of the sample standard deviation

Hi, all

Does anyone let me know the formula for "the standard error of the sample standard deviation" when no specific distribution is assumed for an i.i.d random sequence? I also want to know a (famous if possible) reference book or paper.

Thanks a lot for your help.

2. There is some helpful info here... http://mathworld.wolfram.com/SampleV...tribution.html

If you really need a reference in a book... off the top of my head I know that in an exercise at the end of (chapter 4? maybe 5?) in Casella and Berger you're asked to show that the var(s^2) is what it is so you'd have the final result there.

3. Thanks Dason for reminding the useful textbook
it is in the problem 5.8, page 257
In part a) we are asked to show
, and use this result to derive

Also note that since is an unbiased estimator of ,
the mean squared error and the variance is the same. See
http://en.wikipedia.org/wiki/Mean_sq...error#Examples

I have gone through a quite tedious way, which lead to the same result:
(you can expand the answer above to see)

Therefore,

4. This short article may also be of some help:

http://www.eecs.umich.edu/~fessler/p.../tr/stderr.pdf

5. I'm giving you a thanks BGM because I remember doing that problem and there's no way I would subject myself to that again.

6. Thank you for your perfect lecture.
I would like to appreciate it very much.

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