# [R] Standard error of standard deviation: bootstrap or theoretical results?

huan.huang@bnpparibas.com huan.huang at bnpparibas.com
Wed Aug 6 13:39:29 CEST 2003

```Dear R users,

This is more a statistical question rather than an R question. I'd
appreciate it if you can give me some suggestions.

I have a sample of a time series (sample size 500, fat tail in density). I
am trying to calculate the Standard error of standard deviation of a
sub-block-sample (sample size 250). I take 100 this kind of
sub-block-sample, randomly. For these 100 subsamples, I use the following 3
methods to calculate the standard error of standard deviation:

1. From book "Handbook of applicable mathematics", Walter Ledermann (chief
editor) Volumn VI: Statistics, Part A, Lloyd, John Wiley & Sons.

Page 30-32:

var(S) = (mu4 - mu2^2)/(4 * mu2 * n)
mu4 = E(X - mu)^4, mu2 = E(X - mu)^2, S^2 = sum(X - mu)^2/n

2. From   http://davidmlane.com/hyperstat/A19196.html

3. From   http://mathworld.wolfram.com/StandardDeviationDistribution.html

Finally I calculate the standard deviation for each of the 100 subsamples
and the standard error of those 100 standard deviations ( I reckon this is
the bootstrap result for the standard error of the standard deviation I
want).
I get 0.00024

I tried all above a couple of times and got similar results for each
methods I used. The results from the first 3 methods are apparently higher
than the bootstrap one. I am a bit confused. Do I miss anything? Which one
do you believe?

Thanks a lot.

Huan

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