- #1

- 12

- 0

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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter rhz
- Start date

- #1

- 12

- 0

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

Science Advisor

- 7,968

- 507

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

nσ

cov(k,j) is the covariance of X

- #3

- 12

- 0

_{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}.

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.

- #4

mathman

Science Advisor

- 7,968

- 507

Fix your latex!!!

Share: