I am trying to understand how the precision matrix changes under the influence of small changes in the covariance matrix. I have several similar datasets: the differences in standard deviation for the same variable over different samples are neglegible, while the differences in corralation are mostly not significantly different. As a result, the covariance matrix is only slightly different for different samples, as is the inverse.
But is this always the case? Is there any way of knowing (save for simulation) how much the covariance matrix can change before it's inverse, the precision matrix, changes significantly? Are there any theories and/or literature on this?
