I have a couple of questions related to estimation of high-dimensional precision matrix (inverse of the covariance matrix) in the case where p is close to 100 and n < p. As a measure of estimation accuracy I am calculating a 'relative squarred error' defined in the following manner: $$ RSE(\Sigma^{-1},\hat{\Sigma^{-1}}) = \frac{||{\Sigma^{-1}-\hat{\Sigma^{-1}}}||}{||\Sigma^{-1}||} $$
where, $||A|| = \sum_{i,j}a_{ij}^2 $ is the Frobenius norm of $A$. Now, my questions are,
a) Is there any known result for lower bound of Frobenius norm of a precision matrix? or for that matter, any general matrix?
b) What are the common ways of showing the estimation accuracy of a method. I think we can of course calculate various norms such as the spectral norm etc, but, is there a graphical way of doing this?
I appreciate any kind of help and apologies in advance if this is not the right place or way to ask such questions.
