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Re: Standard error of variance
Posted:
Sep 10, 2013 10:57 PM


For a normal distribution, using the results in http://web.eecs.umich.edu/~fessler/papers/files/tr/stderr.pdf, suppose the sample standard deviation if defined by s = sqrt(s^2).
Then the exact standard error of s is
SE(s) = sigma*sqrt(V)/sqrt(N1),
where V = 2*[{(N1)/2}  {Gamma(N/2)/Gamma((N1)/2)}^2] sigma is the population sigma and Gamma is the gamma function.
For N large, SE(s) is approximately
SE(s) ~~ sigma/sqrt(2(N1))
Note that the standard error of s is proportional to sigma.



