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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

- Thread starter rhz
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- #1

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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

mathman

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Take expectation and subtract out the mean squared and you will have:

nσ

cov(k,j) is the covariance of X

- #3

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Hi,_{k})^{2}= ∑∑X_{k}X_{j}

Take expectation and subtract out the mean squared and you will have:

nσ^{2}+ ∑∑(k≠j) cov(k,j)

cov(k,j) is the covariance of X_{k}X_{j}.

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.

- #4

mathman

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Fix your latex!!!

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