How minimizing the determinant of the information matrix is equivalent to maximizing the differential Shannon entropy? A similar question was posted in Math SE but hasn't been rigorously answered.
My understanding is: By minimizing the determinant of information matrix, we are trying to minimize the deviation of our estimator from the true distribution because ideally a 0 determinant implies singularity or the 0 deviation of the estimator from the actual distribution. (Is this right understanding? If so then the following question arises)
Question: How does this relate to maximizing differential Shannon entropy? How are we maximizing information?