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Sample standard deviation serially correlated normal data

  1. Oct 27, 2011 #1

    rhz

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    Hi,

    Can anyone point me to a reference for the statistical properties of the sample standard deviation of a sequence of identically distributed normal random variables subject to some form of serial correlation?

    Thanks,

    rhz
     
  2. jcsd
  3. Oct 27, 2011 #2

    mathman

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    ( ∑ Xk)2 = ∑∑XkXj
    Take expectation and subtract out the mean squared and you will have:

    2 + ∑∑(k≠j) cov(k,j)

    cov(k,j) is the covariance of XkXj.
     
  4. Oct 27, 2011 #3

    rhz

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    Hi,

    OK, but I'm interested in the statistical properties of the sample standard deviation:

    \sqrt{\hat\sigma^2} = \sqrt \left ( \frac{1}{N-1}\sum^{N-1}_{i=0}(x_i-\hat{\mu})^2 \right )
    \hat\mu = \frac{1}{N}\sum^{N-1}_{i=0}x_i

    Thanks.
     
  5. Oct 28, 2011 #4

    mathman

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    Fix your latex!!!
     
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