I want to estimate the Covariance Matrix for a multidimensional gaussian distribution. My research so far has led me to the conclusion that the method of moments is the most appropriate solution for my case.
I already found that it is unbiased $E[\sigma_{\text{estimated}}] = \sigma_{\text{actual}}$. Now I need to know how many samples I need for a "good enough" accuracy. So I need some relationship between the number of samples and the variance of the estimate of the covariance matrix (so like $E[Var^2]-E[Var]^2$) or some other measure for the accuracy of the estimated variance.
Any ideas or links?
Any help is appreciated, thank you!