- #1
phonic
- 28
- 0
Does anyone know how to calculate the variance of the variance estimator of normal distribution?
x_i, i\in\{1,2,...,n\} are n samples of normal distribtuion N(\mu, \sigma^2).
And S^2 = \frac{n}{n-1} \sum_i (x_i - \bar x)^2 is the variance estimator, where
\bar x = \frac{1}{n} \sum_i x_i.
The question is how to calculate the following variance:
<br /> E[(S^2- \sigma^2)^2]<br />
Where the expectation is respect to sample x_i.Thanks a lot!
x_i, i\in\{1,2,...,n\} are n samples of normal distribtuion N(\mu, \sigma^2).
And S^2 = \frac{n}{n-1} \sum_i (x_i - \bar x)^2 is the variance estimator, where
\bar x = \frac{1}{n} \sum_i x_i.
The question is how to calculate the following variance:
<br /> E[(S^2- \sigma^2)^2]<br />
Where the expectation is respect to sample x_i.Thanks a lot!
Last edited:
