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Help on Variance of Variance

  1. Oct 25, 2005 #1
    Does anyone know how to calculate the variance of the variance estimator of normal distribution?

    [tex] x_i, i\in\{1,2,...,n\} [/tex] are n samples of normal distribtuion [tex]N(\mu, \sigma^2)[/tex].

    And [tex]S^2 = \frac{n}{n-1} \sum_i (x_i - \bar x)^2[/tex] is the variance estimator, where
    [tex] \bar x = \frac{1}{n} \sum_i x_i [/tex].

    The question is how to calculate the following variance:
    E[(S^2- \sigma^2)^2]
    Where the expectation is respect to sample [tex]x_i[/tex].

    Thanks a lot!
    Last edited: Oct 25, 2005
  2. jcsd
  3. Oct 28, 2005 #2


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    I am pretty sure that one can find this explained in an intermediate probability textbook like Mood, Graybill & Boes.
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